9th ibmo - brazil 1994/q2.
Source: 9th ibero Fortaleza-ceara, Brazil, September 17th - 25th
May 7, 2006
geometryrectangleinradiusincenterratiotrigonometryperimeter
Problem Statement
Let a cuadrilateral inscribed in a circumference. Suppose that there is a semicircle with its center on , that
is tangent to the other three sides of the cuadrilateral.
(i) Show that AB \equal{} AD \plus{} BC.
(ii) Calculate, in term of x \equal{} AB and y \equal{} CD, the maximal area that can be reached for such quadrilateral.