Geometry Problems, Online Education

Problem 525: Circles, Diameter, Tangent, Radius, Congruence, Measurement. Level: High School, SAT Prep, College geometry

The figure shows a line ABCD = d with circles C1 of diameter AB and circle C2 of diameter CD. AE and AF are tangent to circle C2, DG and DH are tangent to circle C1. Circle C3 of radius r3 is tangent to C1, AE and AF at B, K and L, respectively. Circle C4 of radius r4 is tangent to C2, DG and DH at C, N and P, respectively. Prove that Formula to prove. See also: Artwork Problem 525.

Circles, tangent, inscribed circles, congruence, similarity

Reference: Fukagawa Hidetoshi, Tony Rothman, "Sacred Mathematics: Japanese Temple Geometry" (Princenton University Press, 2008).

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