Two circles touch at a point \(A\). A common (outer) tangent touching the circles at points \(C\) and \(B\) is drawn. Prove that \(\angle CAB = 90^{\circ}\).
Two circles \(S_1\) and \(S_2\) with centers \(O_1\) and \(O_2\) touch at the point \(A\). A straight line intersects \(S_1\) at \(A_1\) and \(S_2\) at the point \(A_2\). Prove that \(O_1A_1 \parallel O_2A_2\).