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area chasing starting with an equilateral

Source: 2023 Portugal p4 OPM

March 26, 2024
geometryEquilateralareas

Problem Statement

Let [ABC][ABC] be an equilateral triangle and PP be a point on ACAC such that PC‾=7\overline{PC}= 7. The straight line that passes through PP and is perpendicular to ACAC, intersects CBCB at point MM and intersects ABAB at point QQ. The midpoint NN of [MQ][MQ] is such that BN‾=14\overline{BN} = 14. Determine the side of the triangle [ABC][ABC].
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