1994 OIM Problems/Problem 2

Problem

Let there be a quadrilateral inscribed in a circle, whose vertices are denoted consecutively by $A$ , $B$ , $C$ and $D$ . It is assumed that there exists a semicircle with center in $AB$ , tangent to the other three sides of the quadrilateral.

i. Prove that $AB=AD+BC$

ii. Calculate, based on $x=AB$ and $y=CD$ , the maximum area that a quadrilateral that satisfies the conditions of the statement can reach.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

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1994 OIM Problems/Problem 2

Problem

Solution

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