MathDB

2

Part of 2011 Singapore Junior Math Olympiad

Problems(1)

tangent circles, angle bisector wanted (Singapore Junior 2011)

Source:

7/11/2019
Two circles Γ1,Γ2\Gamma_1, \Gamma_2 with radii ri,r2r_i, r_2, respectively, touch internally at the point PP. A tangent parallel to the diameter through PP touches Γ1 \Gamma_1 at RR and intersects Γ2\Gamma_2 at MM and NN. Prove that PRPR bisects ∠MPN\angle MPN.
tangent circlesgeometryangle bisector