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![Online Geometry](h_triangle_center_910.jpg)
Geometry: Incenter, Incircle, Inradius of a triangle, Theorems
and Problems.
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![Incenter, Incircle, Index](incenter_incircle_17.jpg) |
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![Geometry problem 1341](../school-college/4/p1341-isosceles-triangle-80-20-80-bisector-circumcenter-1.jpg) |
Problem 1341.
Isosceles Triangle, 80-20-80 Degrees, Circumcenter, Angle Bisector.
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![Problem 1374 Isosceles Triangle, Circle](../school-college/4/p1374-isosceles-triangle-exterior-cevian-incircle-excircle-parallel-1.jpg) |
Geometry Problem 1374. Isosceles Triangle, Exterior Cevian, Incircle, Excircle, Tangency Points, Parallel Lines. |
![Problem 1373 Isosceles Triangle, Altitude](../school-college/4/p1373-equilateral-triangle-interior-cevian-inradius-exradius-altitude-1.jpg) |
Geometry Problem 1373. Isosceles Triangle, Exterior Cevian, Inradius, Exradius, Altitude to the Base. |
![Problem 1372 Equilateral Triangle, Exterior Cevian, Inradius, Exradius, Altitude](../school-college/4/p1372-equilateral-triangle-exterior-cevian-inradius-exradius-altitude-1.jpg) |
Geometry Problem 1372. Equilateral Triangle, Exterior Cevian, Inradius, Exradius, Altitude, Sketch, iPad Apps. |
![Geometry problem 1351](../school-college/4/p1351-circumscribed-tangential-quadrilateral-midpoint-perpendicular-1.jpg) |
Geometry Problem 1351. Two Tangential or Circumscribed Quadrilaterals, Midpoints, Perpendiculars. |
![Geometry problem 1350](../school-college/4/p1350-triangle-circle-incircle-collinearity-tutor-1.jpg) |
Geometry Problem 1350. Triangle with three Intersecting Circles, Incircle, Collinear Points. |
![Geometry problem 1346](../school-college/4/p1346-equilateral-triangle-incircle-altitude-tutoring-1.jpg) |
Geometry Problem 1346. Equilateral Triangle, Point on the Incircle, Altitude, Perpendicular, Sum of Squares, Distance. |
![Geometry problem 1340](../school-college/4/p1340-scalene-triangle-incenter-circle-isosceles-1.jpg) |
Problem 1340.
Triangle, Incenter, Concentric Circles, Isosceles Triangles, Congruence.
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![Geometry problem 1326](../school-college/4/p1326-triangle-cevian-incircle-angle-270-degree-1.jpg) |
Geometry Problem 1326.
Triangle, Cevian, Incenters, Sum of Angles, 270 Degrees. |
![Geometry problem 1320](../school-college/4/p1320-triangle-incircle-tangent-chord-collinear-1.jpg) |
Geometry Problem 1320.
Triangle, Incircle, Tangent, Chord, Circle, Parallel, Perpendicular, Collinearity. |
![Geometry problem 1316](../school-college/4/p1316-triangle-incircle-chord-sum-segment-congruence-1.jpg) |
Geometry Problem 1316.
Triangle, Incircle, Tangent, Chord, Midpoint, Sum of two Segments, Congruence. |
![Geometry problem 1315](../school-college/4/p1315-triangle-incircle-tangent-chord-congruence-1.jpg) |
Geometry Problem 1315.
Triangle, Incircle, Tangent, Chord, Circle, Congruence. |
![Geometry problem 1314](../school-college/4/p1314-equilateral-triangle-incircle-tangent-congruence-1.jpg) |
Geometry Problem 1314.
Equilateral Triangle, Incircle, Inscribed Circle, Tangent, Congruence. |
![Geometry problem 1309](../school-college/4/p1309-triangle-circle-inradius-exradius-tangent-1.jpg) |
Geometry Problem 1309.
Triangle, Circle, Inradius, Excircle, Tangent, Exradius, Measurement. |
![Geometry problem 1308](../school-college/4/p1308-quadrilateral-diagonal-incircle-tangent-1.jpg) |
Geometry Problem 1308.
Quadrilateral, Diagonal, Triangle, Incircle, Tangent Line, Sides, Measurement. |
![Geometry problem 1307](../school-college/4/p1307-triangle-incenter-parallel-measurement-1.jpg) |
Geometry Problem 1307.
Triangle, Incenter, Parallel line, Sides, Measurement. |
![Geometry problem 1304](../school-college/4/p1304-triangle-120-degrees-angle-bisector-1.jpg) |
Geometry Problem 1304.
Triangle, 120 Degrees, Angle Bisector, Measurement. |
![Geometry problem 1301](../school-college/4/p1301-arbelos-incircle-square-midpoint-1.jpg) |
Geometry Problem 1301.
Arbelos, Semicircles, Diameters, Circle, Incircle, Incenter, Square, Midpoint, Concurrency. |
![Geometry problem 1300](../school-college/3/p1300-arbelos-incircle-tangent-bisector-concurrency-1.jpg) |
Geometry Problem 1300.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Perpendicular, Concurrent Lines. |
![Geometry problem 1298](../school-college/3/p1298-arbelos-incircle-angle-bisector-perpendicular-midpoint-1.jpg) |
Geometry Problem 1298.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector, Perpendicular, Midpoint. |
![Geometry problem 1297](../school-college/3/p1297-arbelos-incircle-tangent-angle-bisector-1.jpg) |
Geometry Problem 1297.
Arbelos, Semicircles, Diameters, Tangent, Circle, Incircle, Angle Bisector. |
![Geometry problem 1295](../school-college/3/p1295-right-triangle-incenter-excenter-angle-1.jpg) |
Geometry Problem 1295.
Right Triangle, Incenter, Incircle, Excenter, Excircle, Congruence, Angle. |
![Geometry problem 1292](../school-college/3/p1292-square-right-triangle-circle-radius-1.jpg) |
Geometry Problem 1292.
Square, Circle, Right Triangle, Arc, Inradius, Radius, Incircle, Measurement. |
![Geometry problem 1288](../school-college/3/p1288-triangle-50-100-degrees-measurement-1.jpg) |
Geometry Problem 1288.
Triangle, 30-50-100 Degrees, Area, Inradius, Metric Relations, Measurement. |
![Geometry problem 1274](../school-college/3/p1274-isosceles-triangle-80-20-80-measurement-1.jpg) |
Geometry Problem 1274.
Isosceles Triangle, 80-20-80 Degrees, Area, Inradius, Circumradius, Angle Bisector, Metric Relations, Measurement. |
![Geometry problem 1271](../school-college/3/p1271-triangle-incircle-excircle-concyclic-tutoring-1.jpg) |
Geometry Problem 1271.
Triangle, Incircle, Incenter, Excircle, Excenter, Escribed Circle, Tangency Points, Six Concyclic Points. |
![Geometry problem 1269](../school-college/3/p1269-triangle-incircle-bisector-90-degree-1.jpg) |
Geometry Problem 1269.
Triangle, Incircle, Incenter, Inscribed Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector. |
![Geometry problem 1267](../school-college/3/p1267-triangle-incircle-excircle-90-degree-parallelogram-1.jpg) |
Geometry Problem 1267.
Triangle, Incircle, Excircle, Circle, Tangency Points, Perpendicular, 90 Degrees, Parallelogram. |
![Geometry problem 1265](../school-college/3/p1265-triangle-incircle-90-degree-bisector-1.jpg) |
Geometry Problem 1265.
Triangle, Incircle, Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector. |
![Geometry problem 1231](../school-college/3/p1231-triangle-orthocenter-circumcenter-incenter-bisector-1.jpg) |
Geometry Problem 1231
Triangle, Orthocenter, Incenter, Circumcenter, Angle Bisector, Center, Circle. |
![Geometry problem 1217](../school-college/3/p1217-triangle-angle-bisector-cyclic-quadrilateral-class-1.jpg) |
Geometry Problem 1217
Triangle, Circle, Excenter, Incenter, Angle Bisector, Cyclic Quadrilateral, Circumcircle, Tangent Line. |
![Geometry problem 1207](../school-college/3/p1207-triangle-incircle-excenter-circumradius-90-degrees-1.jpg) |
Geometry Problem 1207
Triangle, Circle, Incenter, Circumcenter, Excenter, Circumradius, Perpendicular, 90 Degrees. |
![Geometry problem 1206](../school-college/3/p1206-circle-angle-bisector-secant-congruence-area-1.jpg) |
Geometry Problem 1206
Circle, Angle Bisector, Secant, Triangle, Circumcircle, Congruence, Area. |
![Geometry problem 1203](../school-college/3/p1203-right-triangle-angle-bisector-quadrilateral-congruence-1.jpg) |
Geometry Problem 1203
Right Triangle, Square, Angle Bisector, Three Congruent Quadrilaterals. |
![Geometry problem 1191](../school-college/2/p1191-circle-chord-diameter-congruence-bisector-1.jpg) |
Geometry Problem 1191
Circle, Chords, Diameter, Congruence, Midpoint, Collinearity, Bisector. |
![Geometry problem 1180](../school-college/2/p1180-triangle-quadrilateral-120-degrees-bisector-1.jpg) |
Geometry Problem 1180
Quadrilateral, 120 Degrees, Diagonals, Perpendicular. |
![Geometry problem 1178](../school-college/2/p1178-triangle-angle-bisector-metric-relations-1.jpg) |
Geometry Problem 1178
Triangle, Angle Bisector, Metric Relations. |
![Geometry problem 1177](../school-college/2/p1177-triangle-two-angle-bisector-metric-relations-theorem-1.jpg) |
Geometry Problem 1177
Triangle, Two Angle Bisectors, Metric Relations. |
![Geometry problem 1164](../school-college/2/p1164-triangle-cevian-angle-bisector-problem-solving-1.jpg) |
Geometry Problem 1164.
Triangle, Angle Bisector, Cevian. |
![Geometry problem 1174](../school-college/2/p1174-triangle-double-triple-angle-bisector-problem-solving-1.jpg) |
Geometry Problem 1174
Triangle, Quadrilateral, Double, Triple, Angle, Congruence, Excenter, Angle Bisector. |
![Geometry problem 1163](../school-college/2/p1163-isosceles-triangle-double-angle-circle-cyclic-problem-solving-1.jpg) |
Geometry Problem 1163.
Isosceles Triangle, Congruence, Double Angle, Circle, Concyclic Points, Circumcenter, Perpendicular, Angle Bisector. |
![Geometry problem 1153](../school-college/2/p1153-triangle-angle-bisector-perpendicular-congruence-1.jpg) |
Geometry Problem 1153.
Triangle, Angle Bisectors, Perpendicular, Congruence. |
![Geometry problem 1144](../school-college/2/p1144-three-equal-squares-90-degrees-bisector-1.jpg) |
Geometry Problem 1144.
Three Equal Squares, Diagonals, Perpendicular, 90 Degrees, Angle Bisector. |
![Geometry problem 1139](../school-college/2/p1139-triangle-circumcircle-bisector-parallel-90-degrees-concurrent-1.jpg) |
Geometry Problem 1139.
Triangle, Circumcircle, Angle Bisector, Parallel Lines, 90 Degrees, Concurrent Lines. |
![Geometry problem 1199](../school-college/2/p1199-square-equilateral-triangle-circle-metric-relation-1.jpg) |
Geometry Problem 1199
Equilateral Triangle, Square, Altitude, Circle, Incircle, Inradius, Metric Relations. |
![Geometry problem 1181](../school-college/2/p1181-quadrilateral-tangential-cyclic-diameter-problem-solving-1.jpg) |
Geometry Problem 1181
Cyclic Quadrilateral and Tangential Quadrilateral, Diameter as a Diagonal, Incenter, Circumcenter. |
![Geometry problem 1155](../school-college/2/p1155-right-triangle-altitude-incenters-area-1.jpg) |
Geometry Problem 1155.
Right Triangle, Altitude, Incenter, Incircle, Area. |
![Geometry problem 1149](../school-college/2/p1149-isosceles-triangle-cevian-incircles-tangent-congruent-1.jpg) |
Geometry Problem 1149.
Isosceles Triangle, Altitude, Cevian, Incircles, Tangent, Congruence. |
![Geometry problem 1148](../school-college/2/p1148-dynamic-right-triangle-circle-tangent-radius-ipad-animation-1.jpg) |
Dynamic Geometry Problem 1148
Static Geometry Problem 1148.
Right Triangle, Incircle, Circumcircle, Tangent, Radius. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus). |
![Geometry problem 1129](../school-college/2/p1129-isosceles-triangle-incenter-circumcenter-parallel-perpendicular-1.jpg) |
Geometry Problem 1129.
Isosceles Triangle, Circumcenter, Incenter, Parallel Lines, Perpendicular Lines. |
![Geometry Problem 1105](../school-college/2/p1105-triangle-cevian-incircle-excircle-congruence-geometric-mean-math-tutor-1.jpg) |
Geometry Problem
1105.
Triangle, Incircle, Excircle, Cevian, Tangent, Congruence, Geometric Mean. |
![Geometry Problem 1104](../school-college/2/p1104-right-triangle-tangent-circle-radius-math-tutor-1.jpg) |
Geometry Problem
1104.
Right Triangle, Incircle, Circumcircle, Inscribed Circle, Radius,
Tangent. |
![Geometry Problem 1103](../school-college/2/p1103-right-triangle-circle-radius-geometric-mean-math-sangaku-1.jpg) |
Geometry Problem
1103.
Right Triangle, Incircle, Inscribed Circle, Radius, Geometric Mean, Sangaku, Japanese, Metric Relations. |
![Geometry Problem 1102](../school-college/2/p1102-right-triangle-circle-perpendicular-incircle-cathetus-math-1.jpg) |
Geometry Problem
1102.
Right Triangle, Incircle, Tangency Point, 90 Degree, Cathetus, Metric Relations. |
![Geometry Problem 1101](../school-college/2/p1101-triangle-circles-parallel-radius-incircle-math-1.jpg) |
Geometry Problem
1101.
Triangle, Parallel Lines, Circle, Incircle, Inradius, Radius, Angle. |
![Geometry Problem 1081](../school-college/1/p1081-equilateral-triangle-circle-tangent-radius-sangaku-class-math-1.jpg) |
Geometry Problem
1081.
Equilateral Triangle, Inscribed Circle, Inradius, Tangent Circles, Radius, Tangent Line, Sangaku Japanese Problem. |
![Geometry Problem 1068](../school-college/1/p1068-obtuse-triangle-orthocenter-exradius-inradius-circumradius-distance-math-1.jpg) |
Geometry Problem
1068.
Obtuse Triangle, Orthocenter, Circumradius, Inradius, Exradii, Distance, Diameter |
![Geometry Problem 1067](../school-college/1/p1067-triangle-orthocenter-exradius-inradius-circumradius-distance-math-1.jpg) |
Geometry Problem
1067.
Acute Triangle, Orthocenter, Circumradius, Inradius, Exradii, Distance, Diameter. |
![Geometry Problem 1066](../school-college/1/p1066-triangle-obtuse-orthocenter-inradius-circumradius-distance-math-1.jpg) |
Geometry Problem
1066.
Triangle, Obtuse Angle, Orthocenter, Circumradius R, Inradius r, Exradius
ra, Distance, Diameter. |
![Geometry Problem 1065](../school-college/1/p1065-triangle-orthocenter-inradius-circumradius-distance-math-1.jpg) |
Geometry Problem
1065.
Triangle, Acute Angle, Orthocenter, Circumradius R, Inradius r, Exradius
ra, Distance, Diameter. |
![Geometry Problem 1061](../school-college/1/p1061-triangle-inradius-circumradius-circumcircle-bisector-distance-math-1.jpg) |
Geometry Problem
1061.
Triangle, Inradius (r), Circumradius (R), Circumcircle, Angle Bisector, Distance from a point to a Line, Perpendicular. |
![Geometry Problem 1060](../school-college/1/p1060-triangle-incircle-incenter-angle-inscribed-circle-math-1.jpg) |
Geometry Problem
1060.
Triangle, Incircle, Incenter, Inscribed circle, Tangent, Angle. |
![Geometry Problem 1043](../school-college/1/p1043-right-triangle-incenter-excenter-congruence-math-1.jpg) |
Geometry Problem
1043.
Right Triangle, Incenter, Excenter, Congruence, Metric Relations. |
![Geometry Problem 1037](../school-college/1/p1037-triangle-3-equal-circles-incircle-inradius-length-1.jpg) |
Geometry Problem
1037.
Triangle, Three equal Incircles, Tangent lines, Inradius, Length. |
![Geometry Problem 1036](../school-college/1/p1036-triangle-3-equal-circles-incircle-inradius-1.jpg) |
Geometry Problem
1036.
Triangle, Three equal Incircles, Tangent lines, Inradius, Equal Inradii. |
![Geometry Problem 1035](../school-college/1/p1035-triangle-3-equal-circles-incircle-equivalent-area-1.jpg) |
Geometry Problem
1035.
Triangle, Three equal Incircles, Tangent lines, Equivalent triangles, Equal area. |
![Geometry Problem 1034](../school-college/1/p1034-triangle-3-equal-circles-incircle-isoperimetric-1.jpg) |
Geometry Problem
1034.
Triangle, Three equal Incircles, Tangent lines, Isoperimetric triangles, Equal perimeter. |
![Geometry Problem 1024](../school-college/1/p1024-contact-triangle-side-incircle-product-perpendicular-online-math-1.jpg) |
Geometry Problem
1024.
Contact, Gergonne Triangle, Point on an arc of Incircle, Perpendicular, Distances. |
![Geometry Problem 1023](../school-college/1/p1023-contact-triangle-incircle-product-three-perpendicular-online-math-1.jpg) |
Geometry Problem
1023.
Triangle, Contact, Gergonne, Product of three distances. |
![Geometry Problem 1012](../school-college/1/p1012-equilateral-triangle-incenter-perpendicular-concurrent-math-1.jpg) |
Geometry Problem
1012.
Equilateral Triangle, Incenters, Inscribed Circles, Perpendicular, Concurrent Lines. |
![Geometry Problem 991](../school-college/p991-triangle-isosceles-incircle-tangent-midpoint-collinear-1.jpg) |
Geometry Problem 991.
Triangle, Incircle, Tangency Points, Isosceles, Midpoint, Collinearity, Congruence, Circle. |
![Geometry Problem 990](../school-college/p990-triangle-incircle-median-circle-central-angle-congruence-1.jpg) |
Geometry Problem 990.
Triangle, Incircle, Median, Cevian, Central Angle, Congruence, Circle, Secant, Midpoint,
Parallel. |
![Geometry Problem 987](../school-college/p987-triangle-circumcircle-incenter-parallel-circle-tangent-animation-ipad-1.jpg) |
Geometry Problem 987.
Triangle, Circumcircle, Incenter, Chord, Parallel, Circle, Tangent. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus). |
![Geometry Problem 976](../school-college/p976-isosceles-right-triangle-incenter-45-degrees-hypotenuse-1.jpg) |
Geometry Problem 976.
Isosceles Right Triangle, 45 Degrees, Incenter, Angle Bisector, Hypotenuse. |
![Geometry Problem 959](../school-college/p959-triangle-ratio-side-1-4-inradius-exradius-cevian-geometric-mean-1.jpg) |
Geometry Problem 959.
Triangle, Sides Ratio 4:1, Inradius, Exradius, Cevian, Mean Proportional, Geometric Mean, Metric Relations. |
![Geometry Problem 957](../school-college/p957-equilateral-triangle-incircle-circuncircle-circular-segment-area-1.jpg) |
Geometry Problem 957.
Equilateral Triangle, Inscribed Circle, Incircle, Circumscribed Circle, Circumcircle, Area, Circular Segment. |
![Geometry Problem 952](../school-college/p952-triangle-3-equal-circles-tangent-incenter-circumcenter-collinear-1.jpg) |
Geometry Problem 952.
Triangle, Incenter, Circumcenter, Three Equal Circles, Tangent Line, Tangent Circles, Collinear Points. |
![Geometry Problem 943](../school-college/p943-triangle-incircle-parallel-tangency-point-1.jpg) |
Geometry Problem 943.
Triangle, Incircle, Inscribed Circle, Tangency Points, Parallel, Metric Relations. |
![Geometry Problem 942](../school-college/p942-triangle-circumcircle-sagitta-inradius-exradius-1.jpg) |
Geometry Problem 942.
Triangle, Circles, Circumcircle, Sagitta, Incircle, Excircle, Inradius, Exradius, Metric Relations. |
![Problem 935](../school-college/p935-equal-incircles-circles-triangle-cevian-1.jpg) |
Geometry Problem 935.
Square, Circle, Center, Perpendicular, Metric Relations.
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![Problem 921](../school-college/p921-right-triangle-circumcircle-midpoint-incircle-1.jpg) |
Geometry Problem 921.
Right Triangle, Circumcircle, Arc, Midpoint, Tangency Point, Incircle.
|
![Problem 918](../school-college/p918-infographic-triangle-incenter-perpendicular-metric-relations-1.jpg) |
Geometry Problem 918.
Triangle, Incenter, Incircle, Angle Bisector, Perpendicular, Metric Relations.
|
![Geometry Problem 895](../school-college/p895-triangle-incircle-tangent-parallel-collinear-html5-ipad-1.jpg) |
Geometry Problem 895
Triangle, Incircle, Tangency Points, Parallel line, Collinear Points.
GeoGebra, HTML5 Animation for Tablets |
![Geometry Problem 894](../school-college/p894-triangle-incenter-60-degrees-midpoint-parallel-html5-ipad-1.jpg) |
Geometry Problem 894
Triangle, Angle, 60 degrees, Incenter, Midpoint, Parallel Lines.
GeoGebra, HTML5 Animation for Tablets |
![Geometry Problem 893](../school-college/p893-triangle-circumcenter-incenter-circle-collinear-html5-ipad-1.jpg) |
Geometry Problem 893
Triangle, Circumcircle, Incenter, Circle, Tangent, Collinear Points.
GeoGebra, HTML5 Animation for Tablets |
![Geometry Problem 889](../school-college/p889-carnot-theorem-acute-triangle-inradius-circumradius-html5-ipad-1.jpg) |
Geometry Problem 889
Carnot's Theorem in an acute triangle, Circumcenter, Circumradius, Inradius. GeoGebra, HTML5 Animation for Tablets. |
![Problem 886](../school-college/p886-right-triangle-incenter-bisector-concyclic-geogebra-html5-ipad-1.jpg) |
Geometry Problem 886
Right Triangle, Incenter, Angle Bisector, Perpendicular, 45 Degrees, Concyclic Points, Isosceles Right Triangle. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus). |
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