Triangles: Theorems and Problems 5

Geometry Problem 1388.
Triangle 40-60-80 degree, Incenter, Congruence.

Geometry Problem 1387.
Quadrilateral, Double Angle, Congruence, Isosceles Triangle.

Geometry Problem 1386.
Thabit ibn Qurra (826 -901) Theorem and more conclusions, generalized Pythagorean Theorem to any triangle.

Geometry Problem 1385.
Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, Midpoint, Collinear Points.

Geometry Problem 1384.
Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, 90 Degree.

Geometry Problem 1383.
Triangle, Median, Circle, Chord, Secant, Sum, Product.

Geometry Problem 1381.
Parallelogram, Exterior Point, Triangle, Area.

Geometry Problem 1378.
Parallelogram, Diagonal perpendicular to a side, Distances from a Point to Vertices, Measurement.

Geometry Problem 1377.
Isosceles Triangle, Interior Cevian, Equal Sum of Exradii, Excircle.

Geometry Problem 1376.
Isosceles Triangle, Interior Cevian, Excircles, Tangency Points, Parallel Lines.

Geometry Problem 1375.
Isosceles Triangle, Interior Cevian, Exradius, Excircle, Altitude to the Base.

Geometry Problem 1374.
Isosceles Triangle, Exterior Cevian, Incircle, Excircle, Tangency Points, Parallel Lines.

Geometry Problem 1373.
Isosceles Triangle, Exterior Cevian, Inradius, Exradius, Altitude to the Base.

Geometry Problem 1372.
Equilateral Triangle, Exterior Cevian, Inradius, Exradius, Altitude, Sketch, iPad Apps.

Geometry Problem 1363.
Square, Angle Bisector, Perpendicular, 45 Degrees, Angle, Sketch, iPad Apps.

Geometry Problem 1362.
Equilateral Triangle Inscribed in a Circle, Lunula, Ratio of Areas, Tangent, Sketch, iPad Apps.

Geometry Problem 1361.
Triangle, Two Nine-Point Circles, Feuerbach's Circle, Euler's Circle, Congruent Angles, Sketch, iPad Apps.

Geometry Problem 1360.
Triangle, Nine-Point Circle, Feuerbach's Circle, Euler's Circle, Cyclic Quadrilateral, Concyclic Points, Sketch, iPad Apps.

Geometry Problem 1359.
Triangle, Circumcircle, Congruent Angles, Midpoints.

Geometry Problem 1356.
Quadrilateral, Triangle, Angle, 30 Degrees, Congruence.

Geometry Problem 1355.
Triangle, Midpoint, Median, Circle, Chord, Equal Product of measure of segments.

Geometry Problem 1350.
Triangle with three Intersecting Circles, Incircle, Collinear Points.

Geometry Problem 1349.
Three Squares, 90 Degrees, Perpendicular Lines, Diagonal. Math Infographic.

Geometry Problem 1348.
Three Concentric Circles, Equilateral Triangle, Perpendicular Bisector, Congruence.

Geometry Problem 1347.
Triangle, Angle Bisector, Congruence, Circumcircle, Tangent, Equilateral Triangle.

Geometry Problem 1346.
Equilateral Triangle, Point on the Incircle, Altitude, Perpendicular, Sum of Squares, Distance.

Geometry Problem 1345.
Three Equilateral Triangles, Center, Area, Common Vertex.

Problem 1343.
Triangle, Excircles, Circle, Tangent, Tangency Points, Chord, Perpendicular, 90 Degrees, Collinearity. Machu Picchu in the background.

Problem 1341.
Geometry Problem 1341: Isosceles Triangle, 80-20-80 Degrees, Circumcenter, Angle Bisector.

Problem 1340.
Triangle, Incenter, Concentric Circles, Isosceles Triangles, Congruence.

Problem 1337.
Parallelogram, Diagonals, Circle, Circumcircle, Tangent Line, Triangle, Congruence.

Problem 1336.
Right Triangle, Cevian, Double Angle, Perpendicular, 90 Degrees.

Problem 1334. Square, Kite, Sum of Segments.

Geometry Problem 1329.
Two Squares Side by Side, Parallel, Perpendicular, 90 Degrees, Congruence.

Geometry Problem 1328.
Two Squares Side by Side, Perpendicular, 90 Degrees, Congruence.

Geometry Problem 1327.
Two Squares Side by Side, Perpendicular, 90 Degrees, Angle.

Geometry Problem 1326.
Triangle, Cevian, Incenters, Sum of Angles, 270 Degrees.

Geometry Problem 1324.
Quadrilateral, Diagonal, 45 Degrees, Angle Bisector, Isosceles Triangle, Congruence.

Geometry Problem 1323.
Square, Angle Trisector, Diagonal, Regular Dodecagon, Area, 30-60 degrees.

Geometry Problem 1322.
Triangle, Angle Bisector, Circumcircle, Chord, Secant, Sum of two Angles.

Geometry Problem 1320.
Triangle, Incircle, Tangent, Chord, Circle, Parallel, Perpendicular, Collinearity.

Geometry Problem 1319.
Hexagons, Equilateral Triangles, Center, Midpoints.

Geometry Problem 1318.
Rectangle, Equilateral Triangle, Distances, Perpendicular, Measurement.

Geometry Problem 1317.
Triangle, Excircle, Chord, Tangent, Midpoint, Arc, Sum of two Segments, Congruence.

Geometry Problem 1316.
Triangle, Incircle, Tangent, Chord, Midpoint, Sum of two Segments, Congruence.

Geometry Problem 1315.
Triangle, Incircle, Tangent, Chord, Circle, Congruence.

Geometry Problem 1314.
Equilateral Triangle, Incircle, Inscribed Circle, Tangent, Congruence.

Geometry Problem 1313.
Regular Decagon, Pentadecagon, Equilateral Triangle, Congruence.

Geometry Problem 1312.
Triangle, 60 Degrees, Circle, Circumcenter, Orthocenter, Altitude, Distance, Perpendicular, Measurement.

Geometry Problem 1311.
Inscribed Triangle, Circle, Circumcircle, Concyclic Points, Measurement.

Geometry Problem 1310.
Square, Center, Right Triangle, Area, Measurement.

Geometry Problem 1309.
Triangle, Circle, Inradius, Excircle, Tangent, Exradius, Measurement.

Geometry Problem 1308.
Quadrilateral, Diagonal, Triangle, Incircle, Tangent Line, Sides, Measurement.

Geometry Problem 1307.
Triangle, Incenter, Parallel line, Sides, Measurement.

Geometry Problem 1306.
Cyclic, Inscribed Quadrilateral, Circle, Tangent, Diagonals, Collinear Points.

Geometry Problem 1305.
Triangle, Circumcircle, Angle Bisector, Arc, Perpendicular, Area.

Geometry Problem 1304.
Triangle, 120 Degrees, Angle Bisector, Measurement.

Geometry Problem 1303.
Triangle, 60 Degrees, Angle Bisector, Measurement.

Geometry Problem 1302.
Triangle, Median, Midpoint, Circles, Diameters, Congruence.

Geometry Problem 1301.
Arbelos, Semicircles, Diameters, Circle, Incircle, Incenter, Square, Midpoint, Concurrency.

Geometry Problem 1300.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Perpendicular, Concurrent Lines.

Geometry Problem 1299.
Triangles, Interior Point, Angles, 30 degrees.

Geometry Problem 1298.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector, Perpendicular, Midpoint.

Geometry Problem 1297.
Arbelos, Semicircles, Diameters, Tangent, Angle Bisector.

Geometry Problem 1295.
Right Triangle, Incenter, Incircle, Excenter, Excircle, Congruence, Angle.

Geometry Problem 1294.
Triangle, Altitudes, Four Squares, Center, Midpoint, Concyclic Points.

Geometry Problem 1293.
Triangle, Altitudes, Two Squares, Center, Concurrent Lines, Midpoint.

Geometry Problem 1292.
Square, Circle, Right Triangle, Arc, Inradius, Radius, Incircle, Measurement.

Geometry Problem 1290.
Triangle, Internal Angle Bisector, Median, Parallel, Measurement, Metric Relations.

Geometry Problem 1289.
Triangle, Cevian, Concurrency, Measurement, Metric Relations.

Geometry Problem 1288.
Triangle, 30-50-100 Degrees, Area, Inradius, Metric Relations, Measurement.

Geometry Problem 1287.
Triangle, 40-100-40 Degrees, Congruence, Area, Metric Relations, Measurement.

Geometry Problem 1286.
Triangle, Quadrilateral, 60, 135, 105 Degree Angles, Congruence, Measurement.

Geometry Problem 1285.
Triangle, Quadrilateral, 60, 150, 90 Degree Angles, Congruence, Measurement.

Geometry Problem 1284.
Two Equilateral Triangle, Midpoint, Congruence.

Geometry Problem 1283.
Two Equilateral Triangle, Perpendicular, Midpoint.

Geometry Problem 1282.
Three Squares, Common Vertex, Midpoint, Perpendicular, 90 Degrees.

Geometry Problem 1281.
Triangle, Circle, Diameter, Tangent, Altitude, Congruent Angles.

Geometry Problem 1280.
Quadrilateral, Perpendicular Diagonals, Isosceles Right Triangles, 45 Degrees, Collinear Points.

Geometry Problem 1279.
Parallelogram, Midpoint, Triangle, Area, 3/10.

Geometry Problem 1278.
Square, 3-4-5 Right Triangle, Midpoint.

Geometry Problem 1277.
Equilateral Triangle, Circumcircle, Externally Tangent Circles, Tangent Line, Measurement.

Geometry Problem 1276.
Equilateral Triangle, Circumcircle, Internally Tangent Circles, Tangent Line, Measurement.