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AC+BC = sqrt(2)AB -> O(BMP) tangent to AC.

Source: Spain Mathematical Olympiad 2020 P5

July 15, 2020
geometrySpainlengths

Problem Statement

In an acute-angled triangle ABCABC, let MM be the midpoint of ABAB and PP the foot of the altitude to BCBC. Prove that if AC+BC=2ABAC+BC = \sqrt{2}AB, then the circumcircle of triangle BMPBMP is tangent to ACAC.
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