areaCollegegeometric meanGeometryGeometry Problem 1624incircleinradiusmathematicsright trianglesquare
Geometric Challenge Right Triangle, Incircle, Circumscribed Square, Inradius, Area
Share your proof or solution in the comments below.
Target Audience: K-12, Honors Geometry, and College Mathematics Education.
Click for additional details and full diagram.
Target Audience: K-12, Honors Geometry, and College Mathematics Education.
In Problem 1624, we explore a right triangle and a square circumscribed about its incircle with one side resting on the hypotenuse. The challenge is to prove that the area of the square S and the inradius r satisfy the fundamental geometric mean identity S = 4r² = 2mn, where m and n are the hypotenuse segments adjacent to the square.
Explore the full theorem and illustrated diagram by clicking the image below.
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How to contribute:
Post your step-by-step proof in the comments below. Feel free to:
Post your step-by-step proof in the comments below. Feel free to:
- Describe the theorems applied.
- Share a link to your dynamic construction (GeoGebra, Desmos).
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