MathDB
PM = PS wanted, semicircle with center M

Source: 2022 Austrian Mathematical Olympiad Junior Regional Competition , Problem 3

October 4, 2022
geometryequal segmentssemicircle

Problem Statement

A semicircle is erected over the segment ABAB with center MM. Let PP be one point different from AA and BB on the semicircle and QQ the midpoint of the arc of the circle APAP. The point of intersection of the straight line BPBP with the parallel to PQP Q through MM is SS. Prove that PM=PSPM = PS holds.
(Karl Czakler)
Back to ProblemsView on AoPS