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compurational geo with 2 circumcircles and angle bisector

Source: III Soros Olympiad 1996-97 R2 9.3 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 31, 2024
geometryangle bisector

Problem Statement

In triangle ABCABC, sides CBCB and CACA are equal to aa and bb, respectively. The bisector of the angle ACBACB intersects the side ABAB at the point KK and the circumscribed circle of the triangle at point MM. The circumscribed circle of the triangle AMKAMK intersects for second time the straight line CACA at the point PP. Find the length of the segment APAP.