MathDB
2015 Guts #32

Source:

August 2, 2022
2015Guts Test

Problem Statement

Let ABCABC be a triangle with AB=8AB=8, BC=7BC=7, and AC=11AC=11. Let Γ1\Gamma_1 and Γ2\Gamma_2 be the two possible circles that are tangent to ABAB, ACAC, and BCBC when ACAC and BCBC are extended, with Γ1\Gamma_1 having the smaller radius. Γ1\Gamma_1 and Γ2\Gamma_2 are tangent to ABAB to DD and EE, respectively, and CECE intersects the perpendicular bisector of ABAB at a point FF. What is CFFD\tfrac{CF}{FD}?
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