MathDB

P4

Part of 2020 Iran MO (2nd Round)

Problems(1)

Prove CAD<90

Source: Iran second round 2020 , Day 2, P4

7/15/2020
Let ω1\omega_1 and ω2\omega_2 be two circles that intersect at point AA and BB. Define point XX on ω1\omega_1 and point YY on ω2\omega_2 such that the line XYXY is tangent to both circles and is closer to BB. Define points CC and DD the reflection of BB WRT XX and YY respectively. Prove that the angle ∠CAD\angle{CAD} is less than 90∘90^{\circ}
geometryreflectioncommon tangent