Τετάρτη, 11 Οκτωβρίου 2017

2006 JBMO Shortlist 10

Let ${ABCD}$ be an isosceles trapezoid inscribed in a circle ${C}$ with ${AB // CD, AB = 2CD}$. Let ${Q = AD \cap BC}$ and let ${P}$ be the intersection of the tangents to ${C}$ at ${B}$ and ${D}$. Calculate the area of the quadrilateral ${ABPQ}$ in terms of the area of the triangle ${PDQ}$.

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