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MN^2 = AM x BN , semicircle with diameter AB side of square ABCD

Source: Mathematics Regional Olympiad of Mexico Northeast 2016 P4

September 12, 2022
squaregeometrysemicircle

Problem Statement

Let ABCDABCD be a square. Let PP be a point on the semicircle of diameter ABAB outside the square. Let MM and NN be the intersections of PDPD and PCPC with ABAB, respectively. Prove that MN2=AMā‹…BNMN^2 = AM \cdot BN.
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