The Circumcircle And The TangentsGeometry Level 2
Two circles \(\omega_1\) and \(\omega_2\) intersect at points \(A\) and \(B\). The tangent to \(\omega_1\) passing through \(A\) intersects \(\omega_2\) at \(X\). The tangent to \(\omega_2\) passing through \(A\) intersects \(\omega_1\) at \(Y\). Let \(O\) be the circumcenter of \(\triangle XAY\). Then what is the measure of \(\angle OBA\) in degrees?