MathDB
2013 Team #8: Circles and Points

Source:

March 1, 2013
geometrypower of a pointradical axis

Problem Statement

Let points AA and BB be on circle ω\omega centered at OO. Suppose that ωA\omega_A and ωB\omega_B are circles not containing OO which are internally tangent to ω\omega at AA and BB, respectively. Let ωA\omega_A and ωB\omega_B intersect at CC and DD such that DD is inside triangle ABCABC. Suppose that line BCBC meets ω\omega again at EE and let line EAEA intersect ωA\omega_A at FF. If FC⊥CD FC \perp CD , prove that OO, CC, and DD are collinear.
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