Question 24
Circle $\gamma_1$ centred at $O_1$ intersects circle $\gamma_2$ centred at $O_2$ at $P,Q$. The tangent to $\gamma_2$ at $P$ meets $\gamma_1$ again at $A$, and the tangent to $\gamma_1$ at $P$ meets $\gamma_2$ again at $B$, with $A,B\ne P$. Given $PQ\cdot O_1O_2=PO_1\cdot PO_2$ and acute $\angle APB$, determine $\angle APB$ in degrees.