2018 MPFG Problem 17

Problem

Let $ABC$ be a triangle with $AB = 5$ , $BC = 4$ , and $CA = 3$ . On each side of $ABC$ , externally erect a semicircle whose diameter is the corresponding side. Let $X$ be on the semicircular arc erected on side $BC$ such that $\angle CBX$ has measure $15^{\circ}$ . Let $Y$ be on the semicircular arc erected on side $CA$ such that $\angle ACY$ has measure $15^{\circ}$ . Similarly, let $Z$ be on the semicircular arc erected on side $AB$ such that $\angle BAZ$ has measure $15^{\circ}$ . What is the area of triangle $\Delta XYZ$ ? Express your answer as a fraction in simplest form.

Page

Toolbox

Search

2018 MPFG Problem 17

Problem