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TOT 260 1990 Spring A S4 <ACP =<QCB or <ACP+ <QCB =180^o

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June 8, 2024
geometryanglestrapezoid

Problem Statement

Let ABCDABCD be a trapezium with AC=BCAC = BC. Let HH be the midpoint of the base ABAB and let ℓ\ell be a line passing through HH. Let ℓ\ell meet ADAD at PP and BDBD at QQ. Prove that the angles ACPACP and QCBQCB are either equal or have a sum of 180o180^o.
(I. Sharygin, Moscow)
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