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Three tangent circles

Source: Turkey TST 1990 - P1

September 11, 2013
geometry proposedgeometry

Problem Statement

The circles k1,k2,k3k_1, k_2, k_3 with radii (a>c>ba>c>b) a,b,ca,b,c are tangent to line dd at A,B,CA,B,C, respectively. k1k_1 is tangent to k2k_2, and k2k_2 is tangent to k3k_3. The tangent line to k3k_3 at EE is parallel to dd, and it meets k1k_1 at DD. The line perpendicular to dd at AA meets line EBEB at FF. Prove that AD=AFAD=AF.
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