From a point \(A\) the tangents \(AB\) and \(AC\) are drawn to a circle with center \(O\). Prove that if from the point \(M\) the segment \(AO\) is visible at an angle of \(90^{\circ}\), then the segments \(OB\) and \(OC\) are also visible from it at equal angles.
Two circles have radii \(R_1\) and \(R_2\), and the distance between their centers is \(d\). Prove that these circles are orthogonal if and only if \(d^2 = R_1^2 + R_2^2\).