Many Circles but Still Easy

Level pending

Given a triange \(ABC\) and three distinct points \(X,Y,Z\) on \(BC, AC, AB\) respectively, construct the circumcircles of \(\triangle AYZ, \triangle BXZ, \triangle CXY\) 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 \(\frac{[PQR]}{[ABC]}\).

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