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construction wanted, equilateral inscribed right triangle 1989 Kyiv City MO 8.5

Source:

July 17, 2021
geometryright triangleEquilateralinscribedconstruction

Problem Statement

The student drew a right triangle ABCABC on the board with a right angle at the vertex BB and inscribed in it an equilateral triangle KMPKMP such that the points K,M,PK, M, P lie on the sides AB,BC,ACAB, BC, AC, respectively, and KM∥ACKM \parallel AC. Then the picture was erased, leaving only points A,PA, P and CC. Restore erased points and lines.
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