MathDB

G8

Part of 2021-IMOC

Problems(1)

Prove that AY is tangent to (AEF)

Source: IMOC 2021 G8

8/11/2021
Let PP be an arbitrary interior point of △ABC\triangle ABC, and APAP, BPBP, CPCP intersect BCBC, CACA, ABAB at DD, EE, FF, respectively. Suppose that MM be the midpoint of BCBC, ⊙(AEF)\odot(AEF) and ⊙(ABC)\odot(ABC) intersect at SS, SDSD intersects ⊙(ABC)\odot(ABC) at XX, and XMXM intersects ⊙(ABC)\odot(ABC) at YY. Show that AYAY is tangent to ⊙(AEF)\odot(AEF).
geometrytangent