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Show inequality in triangle

Source: 51 Polish MO 2000 Second Round - Problem 2

April 23, 2018

geometrycircumcircleGeometry inequalitygeometric inequalityPoland

Problem Statement

Bisector of angle

BAC

of triangle

ABC

intersects circumcircle of this triangle in point

D \neq A

. Points

K

and

L

are orthogonal projections on line

AD

of points

B

and

C

, respectively. Prove that

AD \ge BK + CL