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Triangle property [A = 30° yields AT = 2 * BC]

Source: INMO 1995 Problem 1

October 6, 2005
geometrygeometric transformationreflectioncircumcircletrigonometryhomothetyparallelogram

Problem Statement

In an acute angled triangle ABCABC, ∠A=30∘\angle A = 30^{\circ}, HH is the orthocenter, and MM is the midpoint of BCBC. On the line HMHM, take a point TT such that HM=MTHM = MT. Show that AT=2BCAT = 2 BC.
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