1994 OIM Problems/Problem 2
Problem
Let there be a quadrilateral inscribed in a circle, whose vertices are denoted consecutively by 
, 
, 
and 
. It is assumed that there exists a semicircle with center in 
, tangent to the other three sides of the quadrilateral.
i. Prove that 
ii. Calculate, based on 
and 
, the maximum area that a quadrilateral that satisfies the conditions of the statement can reach.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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