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Prove that CAP = 2 CPA

Source: Mediterranean MO 2003

October 31, 2010
trigonometrycalculusderivativeconicshyperbolageometry unsolvedgeometry

Problem Statement

In a triangle ABCABC with BC=CA+12ABBC = CA + \frac 12 AB, point PP is given on side ABAB such that BP:PA=1:3BP : PA = 1 : 3. Prove that ∠CAP=2∠CPA.\angle CAP = 2 \angle CPA.
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