MathDB

6

Part of 2020 LMT Spring

Problems(1)

Spring 2020 Team Round Problem 6

Source:

8/22/2020
Let △ABC\triangle ABC be a triangle such that AB=6,BC=8,AB=6, BC=8, and AC=10AC=10. Let MM be the midpoint of BCBC. Circle ω\omega passes through AA and is tangent to BCBC at MM. Suppose ω\omega intersects segments ABAB and ACAC again at points XX and YY, respectively. If the area of AXYAXY can be expressed as pq\frac{p}{q} where p,qp, q are relatively prime integers, compute p+qp+q.