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ASU 454 All Soviet Union MO 1987 PM=distance circumcenter from angle bis.

Source:

August 7, 2019
Circumcenterangle bisectorgeometrycircumcircledistance

Problem Statement

Vertex BB of the ∠ABC\angle ABC lies out the circle, and the [BA)[BA) and [BC)[BC) beams intersect it. Point KK belongs to the intersection of the [BA)[BA) beam and the circumference. Chord KPKP is orthogonal to the angle bisector of ∠ABC\angle ABC . Line (KP)(KP) intersects the beam BCBC in the point MM. Prove that the segment [PM][PM] is twice as long as the distance from the circle centre to the angle bisector of ∠ABC\angle ABC .
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