MathDB

22

Part of 2014 Harvard-MIT Mathematics Tournament

Problems(1)

2014 Guts #22: Tangent to a Cyclic Quad

Source:

4/21/2014
Let ω\omega be a circle, and let ABCDABCD be a quadrilateral inscribed in ω\omega. Suppose that BDBD and ACAC intersect at a point EE. The tangent to ω\omega at BB meets line ACAC at a point FF, so that CC lies between EE and FF. Given that AE=6AE=6, EC=4EC=4, BE=2BE=2, and BF=12BF=12, find DADA.