Geometric Challenge Geometry Problem 1616: Finding the Missing Segment

Share your proof or solution in the comments below.
Target Audience: K-12, Honors Geometry, and College Mathematics Education.

Problem 1616 presents a challenge in finding a specific segment within a configuration of circles and triangles. This problem tests your ability to identify metric relations and apply synthetic logic to calculate exact lengths.
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Proposed Solution
We invite students, teachers, and enthusiasts to share their proofs. This classic challenge can be approached using synthetic geometry.

How to contribute:
Post your step-by-step proof in the comments below. Feel free to:

• Describe your construction and properties applied (centroid/medians).
• Provide a link to a diagram (GeoGebra, Desmos, etc.) if you have one.

Be the first to submit a formal solution!

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Geometry Problem 1608: Right Triangle Area from Incircle Tangent Segments and Hypotenuse Perpendiculars

Challenging Geometry Problem 1608. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.

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Geometry Problem 1603: Can You Find the Hidden Distance AG?

Challenging Geometry Puzzle: Problem 1603. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.

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Geometry Problem 1590: Triangle, Incenter, Incircle, Tangency Points, Midpoints, Areas

Challenging Geometry Puzzle: Problem 1590. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.

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Garden Geometry 1585: The Hidden Harmony of Paths and Tangent Points

Challenging Geometry Puzzle: Problem 1585. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.

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Geometric Problem1584: Proving a Ratio with the Incircle, Tangency Points, and Angle Bisector

Challenging Geometry Puzzle: Problem 1584. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.

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geometry Problem 1569: Prove the Length of EG Equals the Diameter of the Incircle of Triangle BDE in Isosceles Triangle ABC

Challenging Geometry Puzzle: Problem 1569. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.

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Geometry Problem 1556: Right Triangle ABC and Inscribed Circle.

Challenging Geometry Puzzle: Problem 1556. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.

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Geometry Problem 1549: Calculating Angle BGE with the Incircle and Tangent in Triangle ABC

Geometry Problem 1549. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

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Geometry Problem 1546: Discover the Hidden Geometry: Calculate Area of Contact Triangle DEF in Triangle ABC

Geometry Problem 1546. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

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Geometry Problem 1545: Calculate the Area of Triangle ABC with Inscribed Circle and Excenters

Geometry Problem 1545. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

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Geometry Problem 1503: Triangle, Incircle, Tangent, Congruence, Perpendicular

Geometry Problem 1503. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

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Geometry Problem 1502: Right Triangle, Incircle, Inradius, Geometric Mean of 2 Inradii, Angle Bisector, Perpendicular, Tangential Quadrilateral

Geometry Problem 1502. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

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To post a solution to this problem click Comment underneath the post, or click into the line that says, “Enter Comment.” Type what you want to say and press Publish to post your solution.

Geometry Problem 1492: Right Triangle, Altitude, Incenters, Angle, Measurement

Geometry Problem 1492. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

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Geometry Problem 1491: Cyclic Quadrilateral, Diagonal, Incircle, Angle, Measurement

Geometry Problem 1491. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

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Geometry Problem 1490: Triangle, Cevian, Incircle, Tangent, Measurement

Geometry Problem 1490. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

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Geometry Problem 1486: Right Triangle, Altitude, Incircle, Tangent, Measurement

Geometry Problem 1486. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

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Geometry Problem 1471: Equilateral Triangle, Inside/Outside Point, Incenters, Tangency Points, Concurrent Lines

Interactive step-by-step animation using GeoGebra. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

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Geometry Problem 1470: Tangential Quadrilateral, Incircles, Tangent, Parallel, Rhombus

Interactive step-by-step animation using GeoGebra. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

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Geometry Problem 1465: Tangential Quadrilateral, Incenter, Inscribed Circle, Equal Sum of Areas

Interactive step-by-step animation using GeoGebra. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

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