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 $$\triangle AYZ, \triangle BXZ, \triangle CYZ$$ 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 $$\frac{[PQR]}{[ABC]}$$.

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