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![Go Geometry Education, Tutoring, Tutorial, Tutor](../problem/h_geometry_problem_810.jpg)
Geometry: Open Problems, High School, College, Tutoring
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![Online education degree: Open geometry problems, Tutoring, Tutorial, Tutor](open_problems_i_1.jpg) |
Geometry: Open Problems
Geometry problems from the gogeometry.com website awaiting submission of solutions.
The ultimate goal may be to encourage mathematical thinking and
problem-solving skills, and to foster a sense of community among those
interested in geometry and mathematics more broadly.
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![Geometry Problem 1572](../school-college/6/p1572-using-geometric-principles-solve-angle-in-triangle-given-2-sides-one-angle-class-1.jpg) |
Geometry Problem 1572:
Calculate Angle C with Geometric Methods Using Sides AB=17, BC=25, and Angle A=45 Degrees
Share Your Solution Here |
![Geometry Problem 1571](../school-college/6/p1571-pythagorean-triangle-triple-7-24-25-prove-angle-74-degrees-tutoring-1.jpg) |
Geometry Problem 1571:
Prove that the intermediate angle in a Pythagorean Triple 7-24-25 measures 74 degrees.
Share Your Solution Here |
![Geometry Problem 1570](../school-college/6/p1570-overlapping-two-squares-common-vertex-a-measures-class-1.jpg) |
Geometry Problem 1570:
Calculating BE in Overlapping Squares: A High School and College Geometry Challenge.
Share Your Solution Here |
![Geometry Problem 1569](../school-college/6/p1569-isosceles-triangle-square-relationship-diameter-incircle-tutoring-1.jpg) |
Geometry Problem 1569:
Prove a Relationship: EG Equals the Incircle Diameter in Triangle ABC with Square CDEF.
Share Your Solution Here |
![Geometry Problem 1568](../school-college/6/p1568-proving-concyclicity-in-triangle-with-incircle-and-tangent-circle-problem-solving-tutoring-1.jpg) |
Geometry Problem 1568:
Concyclicity of Points B, D , H, J in a Triangle ABC with an Incircle and a Tangent Circle.
Share Your Solution Here |
![Geometry Problem 1567](../school-college/6/p1567-bases-isosceles-trapezoid-circumscribed-circle-chord-distance-measurement-tangent-tutoring-1.jpg) |
Geometry Problem 1567:
Finding Tangent Distances in a Circumscribed Isosceles Trapezoid.
Share Your Solution Here |
![Geometry Problem 1566](../school-college/6/p1566-equilateral-triangle-cevian-60-degrees-mystery-sum-of-segments-tutoring-1.jpg) |
Geometry Problem 1566:
Demonstrate AC Equals AE + CD in an Equilateral Triangle ABC Involving Cevians and 60 Degrees.
Share Your Solution Here |
![Geometry Problem 1565](../school-college/6/p1565-triangle-median-perpendicular-midpoint-congruence-tutoring-1.jpg) |
Geometry Problem 1565:
Find the Length of BF in Triangle ABC Involving Median, Perpendicular, Midpoint, and Congruence.
Share Your Solution Here |
![Geometry Problem 1564](../school-college/6/p1564-find-area-quadrilateral-in-right-triangle-abc-with-altitude-bisectors-midpoint-tutoring-1.jpg) |
Geometry Problem 1564:
Find the Area of Quadrilateral BGDJ in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints.
Share Your Solution Here |
![Geometry Problem 1563](../school-college/6/p1563-midpoint-mysteries-proving-perpendicularity-in-right-triangle-abc-altitude-bisectors-1.jpg) |
Geometry Problem 1563:
Perpendicularity in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints.
Share Your Solution Here |
![Geometry Problem 1562](../school-college/6/p1562-right-angled-triangle-bisector-midpoint-collinear-points-proof-1.jpg) |
Geometry Problem 1562:
Proof of Collinearity in a Right-angled Triangle involving the Altitude, Angle bisectors, and Midpoint.
Share Your Solution Here |
![Geometry Problem 1558](../school-college/6/p1558-midpoints-of-segments-connecting-corresponding-vertices-of-two-equilateral-triangles-form-an-equilateral-triangle-1.jpg) |
Geometry Problem 1558:
The midpoints of segments connecting corresponding vertices of equilateral triangles form an equilateral triangle.
Share Your Solution Here |
![Geometry Problem 1555](../school-college/6/p1555-circle-chord-intersect-geometry-problem-solving-1.jpg) |
Geometry Problem 1555: Find Length of DE. The problem involves chords, tangent, circles, and intersections of line
Share Your Solution Here |
![Geometry Problem 1553](../school-college/6/p1553-triangle-abc-angle-bisectors-calculate-circumradius-1.jpg) |
Geometry Problem 1553: Solving for OC in Triangle ABC with Unique Angle Bisectors
Share Your Solution Here |
![Geometry Problem 1552](../school-college/6/p1552-triangle-ABC-auxiliary-line-angle-calculation-1.jpg) |
Geometry Problem 1552: Exploring Angle C in Triangle ABC with Given Angle A and Side Lengths
Share Your Solution Here |
![Geometry Problem 1541](../school-college/6/p1541-inscribed-cyclic-quadrilateral-diameter-circumcircle-harmonic-quaternary-menelaus-ceva-1.jpg) |
Geometry Problem 1541 Challenge: Unveiling BG Length in an Inscribed Quadrilateral with Harmonic Quaternary Insight for Academic Pursuit.
Share Your Solution Here |
![Geometry Problem 1540](../school-college/6/p1540-length-chord-circle-intersection-diameter-similarity-math-class-1.jpg) |
Geometry Problem 1540: Solving for the Length of Chord in a Circle: Analyzing Intersections and Given Values for Academic Pursuits.
Share Your Solution Here |
![Geometry Problem 1502](../school-college/6/p1502-rigth-triangle-incircles-measurement-inradius-square-quadrilateral-1.jpg) |
Geometry
Problem 1502.
Share Your Solution Here Right Triangle, Incircle, Inradius, Geometric Mean of 2 Inradii, Angle Bisector, Perpendicular, Tangential Quadrilateral. |
![Geometry Problem 1498](../school-college/5/p1498-intersecting-circles-diameter-common-chord-secant-cyclic-quadrilateral-concyclic-collinear-points-1.jpg) |
Geometry
Problem 1498.
Share Your Solution Here Intersecting Circles, Diameter, Common Chord, Secant, Cyclic Quadrilateral, Concurrent Lines, Concyclic and Collinear Points. |
![Geometry Problem 1496](../school-college/5/p1496-triangle-double-angle-isosceles-30-degree-congruence-1.jpg) |
Geometry
Problem 1496.
Share Your Solution Here Triangle, Congruence, Isosceles, Double Angle, 30 Degrees. |
![Dynamic Geometry 1480](../school-college/5/p1480-cyclic-polygon-triangulation-sum-inradii-invariant-geogebra-ipad-1.jpg) |
Dynamic Geometry 1480.
Share Your Solution Here Japanese Theorem for Cyclic Polygon,
Sangaku, Triangulation, Non-intersecting Diagonals, Sum of Inradii, Invariant, Step-by-step Illustration. GeoGebra,
iPad. |
![Dynamic Geometry 1475](../school-college/5/p1475-clifford-intersecting-circles-theorem-geogebra-1.jpg) |
Dynamic Geometry 1475.
Share Your Solution Here Clifford Intersecting Circles Theorem, Step-by-step Illustration, GeoGebra, iPad. |
![Dynamic Geometry 1473](../school-college/5/p1473-kosnita-theorem-triangle-circumcenter-concurrent-geogebra-1.jpg) |
Dynamic Geometry 1473.
Share Your Solution Here
Kosnita's Theorem, Triangle, Four Circumcenters, Concurrent Line, Step-by-step Illustration. |
![Dynamic Geometry 1471](../school-college/5/p1471-equilateral-triangle-incenter-concurrent-geogebra-ipad-1.jpg) |
Dynamic Geometry 1471.
Share Your Solution Here
Equilateral Triangle, Inside/Outside Point, Incenters, Tangency Points, Concurrent Lines, Step-by-step Illustration. |
![Dynamic Geometry 1470](../school-college/5/p1470-tangential-quadrilateral-circle-rhombus-geogebra-1.jpg) |
Dynamic Geometry 1470.
Share Your Solution Here
Tangential Quadrilateral, Incircles, Tangent,
Parallel, Rhombus, Step-by-step Illustration. |
![Geometry Problem 1461](../school-college/5/p1462-newton-theorem-gauss-line-quadrilateral-midpoint-side-diagonal-geogebra-1.jpg) |
Geometry Problem 1462.
Share Your Solution Here
Newton-Line, Newton-Gauss Line, Complete Quadrilateral, Midpoints of Sides and Diagonals,
Collinear Points. |
![Geometry Problem 1460](../school-college/5/p1460-newton-gauss-line-dynamic-complete-quadrilateral-1.jpg) |
Dynamic Geometry
1460.
Share Your Solution Here
Newton-Gauss Line, Complete Quadrilateral, Midpoints of Diagonals,
Collinear Points, Step-by-step Illustration using GeoGebra. |
![Geometry Problem 1458](../school-college/5/p1458-incircle-excircle-triangle-area-1.jpg) |
Geometry
Problem 1458.
Share Your Solution Here
Triangle, Incircles, Excircle, Area, Step-by-step Illustration using GeoGebra. |
![Dynamic Geometry 1451](../school-college/5/p1451-orthopole-geogebra-triangle-perpendicular-concurrency-1.jpg) |
Dynamic Geometry 1451.
Share Your Solution Here
Orthopole of a Line. Step-by-step
illustration using GeoGebra. |
![Dynamic Geometry 1450](../school-college/5/p1450-ortholine-complete-quadrilateral-geogebra-dynamic-igs-1.jpg) |
Dynamic Geometry 1450.
Share Your Solution Here
Ortholine, Steiner Line, Complete Quadrilateral, Collineal Orthocenters. Step-by-step
illustration using GeoGebra. |
![Dynamic Geometry 1449](../school-college/5/p1449-salmon-line-geogebra-dynamic-geometry-igs-1.jpg) |
Dynamic Geometry 1449.
Share Your Solution Here
Salmon Line. Step-by-step
illustration using GeoGebra. |
![Problem 1444](../school-college/5/p1444-asymmetric-propeller-equilateral-triangle-geogebra-1.jpg) |
Dynamic Geometry Problem 1444.
Share Your Solution Here
The Asymmetric Propeller Theorem, Equilateral Triangles, Midpoints. Using GeoGebra. |
![Problem 1437](../school-college/5/p1437-circle-intersecting-tangent-equal-product-ipad-sw-typography-1.jpg) |
Geometry Problem 1437.
Share Your Solution Here
Intersecting Circles, Common Tangent, Equal Product, Art, Poster, Typography, iPad Apps. |
![Problem 1435](../school-college/5/p1435-circle-diameter-tangent-parallelogram-1.jpg) |
Geometry Problem 1435.
Share Your Solution Here
Circle, Diameter, Inscribed Circles, Circular Sector, Parallelogram, Parallel Lines, Tangency Points,
Poster, Typography, iPad Apps. |
![Problem 1434](../school-college/5/p1434-equilateral-triangle-tangent-circles-line-1.jpg) |
Geometry Problem 1434.
Share Your Solution Here
Equilateral Triangle, Tangent Circles, Tangent Lines, Arithmetic Mean, Measurement,
Poster, Typography, iPad Apps. |
![Problem 1431](../school-college/5/p1431-apollonius-llc-triangle-circumcircle-tangent-congruent-angle-1.jpg) |
Geometry Problem 1431.
Share Your Solution Here
Triangle, Circumcircle, Parallel Chord, Apollonius, LLC, Congruent Angles, Poster, Conformal Mapping. |
![Problem 1417](../school-college/5/p1417-triangle-incenter-circumcircle-tangent-cevian-bisector-perpendicular-1.jpg) |
Geometry Problem 1417.
Share Your Solution Here
Triangle, Cevian, Circumcircle, Incenter, Perpendicular, Angle Bisector,
Tangent Lines, Tangent Circles. |
![Problem 1401](../school-college/5/p1401-rigth-triangle-isosceles-tangent-congruence-tutor-1.jpg) |
Geometry Problem 1401.
Share Your Solution Here
Right Triangle with three circles on the sides, Isosceles, Diameter, Center, Tangent, Congruence. |
![Problem 1396](../school-college/4/p1396-triangle-rectangles-perpendicular-concurrency-1.jpg) |
Geometry Problem 1396.
Share Your Solution Here
Triangle with three rectangles on the sides, Vertices, Perpendicular lines, Concurrency. |
![Problem 1388 Circle, Triangle](../school-college/4/p1385-triangle-circumcircle-orthocenter-bisector-collinear-1.jpg) |
Geometry Problem 1385.
Share Your Solution Here
Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, Midpoint, Collinear Points. |
![Problem 1376 Isosceles Triangle, Circle](../school-college/4/p1376-isosceles-triangle-interior-cevian-exradius-parallel-1.jpg) |
Geometry Problem 1376.
Share Your Solution Here
Isosceles Triangle, Interior Cevian, Excircles, Tangency Points, Parallel Lines. |
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Last updated:
Jul 26, 2024
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