Geometry Problems: High School, College

Geometry Problems 1-100

 

Geometry Problems 1-100

Online education degree: Open geometry problems

Open Geometry Problems - Index

Triangle, median, angles, degree

Problem 1.
Triangle, median, angles, 45 degrees.

Triangle, angles

Problem 2.
Triangle, angles, 10, 20 , 30 , 80 degrees.

Triangle, Angles, 45 degrees, Auxiliary Lines

Problem 3.
Triangle, Angles, 45 degrees, Auxiliary Lines.

Quadrilateral, equal sides, angles, 120 degrees

Problem 4.
Quadrilateral, equal sides, angles, 120 degrees.

Problem 5.
Triangle, cevian, equal segments, angles, cevian.

Triangle, congruence, angles

Problem 6.
Triangle, cevian, equal segments, and angles.

Triangle, cevian, congruence, and angles

Problem 7.
Triangle, cevian, congruence, and angles.

Triangles, equal segments, angles, 45 degrees

Problem 8.
Triangles, equal segments, angles, 45 degrees.

Triangles, equal segments, angles, 30 degrees

Problem 9.
Triangles, equal segments, angles, 30 degrees.

Triangle, cevian, equal segments, angles, 80-20 degrees

Problem 10.
Triangle, cevian, equal segments, angles, 80-20 degrees.

Right triangle, angles, degreees

Problem 11.
Right triangle, cevian, angles, degrees.

Triangle, Congruence, ANgle, Degrees

Problem 12.
Triangle, cevian, equal segments, angles, degrees.

Triangle, cevian, congruence, angle, degrees

Problem 13.
Triangle, cevian, congruence, angles, degrees.

Triangle, Congruence, Angles

Problem 14.
Triangle, median, angles, degrees.

Triangle, cevian, angle, 30 degrees

Problem 15.
Triangle, cevian, sum of segments, angles, angle bisector, 30 degrees.

Triangle, cevian, perpendicular, angle

Problem 16.
Triangle, cevian, perpendicular, angles, angle bisector, degrees.

Right triangle, angle, altitude, degrees

Problem 17.
Right triangle, altitude, and angles.

Right triangle, cevian, angle, congruence

Problem 18.
Right triangle, cevian, and angles.

Right triangle, excenter, perpendicular, congruence

Problem 19.
Isosceles Right triangle, perpendicular, Excenter, Congruence.

Right triangle, altitude, incircle, inradii

Problem 20.
Right triangle, altitude, incircles and inradii.

Acute triangle, orthocenter, diameter, tangents

Problem 21.
Acute triangle, orthocenter, diameter, tangents.

Right triangle, altitudes, incircles and inradius

Problem 22.
Right triangle, altitudes, incircles and inradii.

Right triangle, altitude, incircles and inradius

Problem 23.
Right triangle, altitude, incircles and inradii.

Right triangle, altitude, incircles and inradii

Problem 24.
Right triangle, altitude, incircles and inradii.

Right triangle, altitude, incircles, angle bisector

Problem 25.
Right triangle, altitude, incircles and inradius.

Right Triangle, altitude, incircles and inradius

Problem 26.
Right Triangle, altitude, incircles and inradius.

Right Triangle, incircles and inradius

Problem 27.
Right Triangle, incircles and inradius.

Right Triangle, altitude, incircles and inradius

Problem 28.
Right Triangle, altitude, incircles and inradius.

Right Triangle, altitude, incircle and inradius. Ten conclusions

Problem 29.
Right Triangle, altitude, incircle and inradius. Ten conclusions.

Right triangle, incenter, inradius 

Problem 30.
Right Triangle, Incircle, Inradius.

Triangle, Incenter, Collinearity

Problem 31.
Right Triangle, Incircle, Collinears.

Triangle, Incircles, Tangents, Cevian

Problem 32.
Triangle, Cevian, Incircles, Tangents.

Triangle, Quadrilateral, Angles

Problem 33.
Triangle and quadrilateral.

Right triangle, Cevian, Incircles, Tangents and Inradius

Problem 34.
Right triangle, Cevian, Incircles, Tangents and Inradius.

Cyclic quadrilateral

Problem 35.
Incenters and Inradii in Cyclic Quadrilateral.

Right triangle, altitude

Problem 36.
Right triangle, altitude, incircles and inradii.

Right triangle, altitude, orthocenter, incenter, incircle

Problem 37.
Right triangle, altitude, incircles, incenters, and orthocenter.

Right triangle, altitude, incircles, incenters, and angles

Problem 38.
Right triangle, altitude, incircles, incenters, and angles.

Triangle, Incircle, Bisector, Cyclic Quadrilateral, Angle

Problem 39.
Triangle, Incircle, Bisector, Cyclic Quadrilateral and angles.
Problem 39 Geometry Help.
Facts you should know for the proposed problem 39.

Triangle, incenter, excenter, 80, 40 degrees 

Problem 40.
Triangle, Incenter, Excenter, Angles 80, 40, Distances.
Problem 40. Geometry Help. Suggestions.

Three tangent circles, radius, common tangent

Sangaku Problem 41.
"Mickey Mouse." Three circles, tangents, radii.

Angles equal segments, and triangles, 30-60 degrees

Problem 42.
Angles, equal segments, and triangles, 30-60 degrees.

Angles equal segments, and triangles, 30-60 degrees

Problem 43.
Angles equal segments, and triangles, 30-60 degrees.

Angles and triangles, 30-60 degrees.

Problem 44.
Angles and triangles, 30-60 degrees.

Angles and triangles, 30-60 degrees

Problem 45.
Angles and triangles, 30-60 degrees.

Triangle, median, and angles, 30 degrees

Problem 46.
Triangle, median, and angles, 30 degrees.

Triangle, median, and angles, 15, 30 degrees

Problem 47.
Triangle, median, and angles, 15, 30 degrees.

Angles and triangles, 30 degrees

Problem 48.
Angles and triangles, 30 degrees.

Right triangle, cevian, perpendicular, and angles

Problem 49
Right triangle, cevian, perpendicular, and angles.

Triangle with Equilateral triangles. 17 Propositions 

Problem 50.
Triangle with Equilateral triangles. 17 Propositions

Problem 51: Fagnano's Problem
Inscribed Triangle with the Minimum Perimeter.

Problem 52
Triangle, angles, incircle.

Geometry problem 53 angle bisector

Problem 53: Angle bisector, circles

Problem 54 Angle bisector, circles, midpoint of arc

Problem 54: Angle bisector, circles Midpoint of arc.

Problem 55 Angle bisector, circle, cyclic quadrilateral

Problem 55: Angle bisector, circles Cyclic Quadrilateral.

Problem 56 Angle bisector, circle parallel lines

Problem 56: Angle bisector, circles Parallel Lines.

Problem 57  Angle bisector, circles, cyclic quadrilateral

Problem 57: Angle bisector, circles Cyclic Quadrilateral.

Problem 58: Right Triangle, Congruence, Perpendiculars.

Problem 59: Right and Equilateral Triangles, Midpoints..

 

Problem 60: Isosceles triangle.

Proposed Problem 61:
Triangle, Trisection of Sides, Perimeter.

Proposed Problem 62:
Square Diagonal, Inscribed Circle, Arc, 90 degrees.

Proposed Problem 63:
Heptagon Regular, Side and Diagonals.

Proposed Problem 64: Triangle, Incircle, Transversal.

Proposed Problem 65: Right Triangle, Mindpoints.

Proposed Problem 66: Triangle, Excircle, Tangents, Geometric Mean.
 

Proposed Problem 67: Triangle, Circumcircle, Angles, Cyclic Quadrilateral.
 

Proposed Problem 68

Proposed Problem 68: Triangle, Incircle, Inradius, Tangent, Similarity.

Proposed Problem 69: Square inscribed in a triangle, Similarity.

Proposed Problem 70: Squares inscribed in a triangle, Similarity.

 

Proposed Problem 71: Cyclic Quadrilateral.
Angles.

Proposed Problem 72: Intersecting Circles.
Cyclic quadrilateral, Chords, Parallel.

 

Proposed Problem 73: Three Intersecting Circles. Cyclic quadrilateral.

 

Proposed Problem 74: Three Intersecting Circles. Cyclic quadrilateral, Angles.

Proposed Problem 75: Three Intersecting Circles. Cyclic quadrilateral, Angles.
Acquire and demonstrate mathematical reasoning ability when solving problems.

Proposed Problem 76: Area of a Circle. Square, Circle, Circular Sector.

Math Problem 77 Angles

Proposed Problem 77: Angles of a Circle. Parallel lines, Cyclic quadrilateral.

Proposed Problem 78: Angles of a Circle. Perpendicular and parallel lines, Midpoint, Diameter, Chord, Cyclic quadrilateral, Congruence.

Proposed Problem 79: Triangle. Similarity, Altitudes, Orthocenter, Incircles, Inradii.

Proposed Problem 80. Area of a triangle, side, incircle, inradius.

Triangle area

Proposed Problem 81. Area of a triangle, side, inradius, circumradius.

Contact triangle area

Proposed Problem 82. Area of the Contact Triangle, inradius, circumradius.

Proposed Problem 83. Area of the Excircle Contact Triangle, exradius, circumradius.

Proposed Problem 84. Contact Triangles Areas, Incircle, Excircle, Inradius, Exradius.

Proposed Problem 85. Contact Triangles Areas, Incircle, Excircle.

Proposed Problem 86. Intouch and Extouch Triangles, Areas.

Quadrilateral area problem

Proposed Problem 87. Area of Quadrilaterals and Midpoints of Diagonals.

Math problem

Proposed Problem 88. Triangle and Quadrilateral Areas, Midpoints.

Math problem

Proposed Problem 89. Triangles of equal area, Midpoints.

Geometry problem

Proposed Problem 90. Quadrilateral and Triangle Areas, Midpoints.

Elearning 91

Proposed Problem 91. Similar Triangles, Altitude, Parallel.

Elearning Problem 92

Proposed Problem 92. Similar Triangles, Circumcircles, Circumradii, Parallel.

Elearning 93 Parallelogram

Proposed Problem 93. Similar Triangles, Circumcircles, Parallelogram.

Problem 94, Elearning

Proposed Problem 94. Similar Triangles, Circumcircles, Circumradii.

Problem 95, Elearning

Proposed Problem 95. Similar Triangles, Inradii, Parallel.

Elearning 96

Proposed Problem 96. Similar Triangles, Incenters, Parallelogram.

Elearning 97

Proposed Problem 97. Similar Triangles, Areas.

Quadrilateral Area, Elearning.

Proposed Problem 98. Quadrilateral Area, Centroid, Similarity.

Circle area and Pythagoras

Proposed Problem 99: Circle Area, General Extension to Pythagoras' Theorem.

Circle area problem. Elearning 100

Proposed Problem 100. Circle Area, Archimedes' Book of Lemmas.




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