College MathematicsCurvilinear IncirclesGeometryGeometry ProblemsHigh School MathProblem 1627Synthetic GeometryTangent Circles
Three Mutually Tangent Circles, Collinear Centers, and Curvilinear Incircle Radii Relations
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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 1627, we explore three mutually tangent circles with collinear centers and a common external tangent line. The challenge is to prove using synthetic similarity that the radii satisfy a geometric progression, and to establish the elegant radical and harmonic difference relations involving the radii of their curvilinear inscribed circles.
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Post your step-by-step proof in the comments below. Feel free to:
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