# Many Circles but Still Easy

Given a triange \(ABC\) and three distinct points \(X,Y,Z\) on \(BC, AC, AB\) respectively, construct the circumcircles of \(\triangle AYZ, \triangle BXZ, \triangle CYZ\) and call these circles \(\alpha, \beta, \gamma\) respectively. Let the intersection of circles \(\alpha - \beta, \alpha - \gamma, \beta - \gamma\) be \(P, Q, R\) with \(P,Q,R \neq X,Y,Z\). Find \(\frac{[PQR]}{[ABC]}\).