MathDB
Problem 3

Source: Paraguayan Mathematical Olympiad 2006

July 22, 2015
geometry

Problem Statement

Let ΓA\Gamma_A, ΓB\Gamma_B, ΓC\Gamma_C be circles such that ΓA\Gamma_A is tangent to ΓB\Gamma_B and ΓB\Gamma_B is tangent to ΓC\Gamma_C. All three circles are tangent to lines LL and MM, with AA, BB, CC being the tangency points of MM with ΓA\Gamma_A, ΓB\Gamma_B, ΓC\Gamma_C, respectively. Given that 12=rA<rB<rC=7512=r_A<r_B<r_C=75, calculate:
a) the length of rBr_B. b) the distance between point AA and the point of intersection of lines LL and MM.
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