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perimeter of triangle wanted (V Soros Olympiad 1998-99 Round 3 9.10)

Source:

May 25, 2024
ratiogeometryperimeter

Problem Statement

The bisector of angle ∠BAC\angle BAC of triangle ABCABC intersects arc BCBC (not containing point AA) of the circle circumscribed around this triangle at point PP. Segment APAP is divided by side BCBC in ratio kk (counting from vertex AA). Find the perimeter of triangle ABCABC if BC=aBC = a.
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