Let ABC be a triangle with circumcircle Ω, and let P be a point on the arc BC of Ω not containing A. Let ωB and ωC be circles respectively passing through B and C and such that both of them are tangent to line AP at point P. Let R, RB, RC be the radii of Ω, ωB, and ωC, respectively.
Prove that if h is the distance from A to line BC, then
RRB+RC≤hBC. geometrycircumcirclegeometric inequalityinequalities