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computational with distances of a points from triangle sides in

Source: Dutch NMO 2006 p2

September 21, 2019
geometryaltitudealtitudes

Problem Statement

Given is a acute angled triangle ABCABC. The lengths of the altitudes from A,BA, B and CC are successively hA,hBh_A, h_B and hCh_C. Inside the triangle is a point PP. The distance from PP to BCBC is 1/3hA1/3 h_A and the distance from PP to ACAC is 1/4hB1/4 h_B. Express the distance from PP to ABAB in terms of hCh_C.
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