Prove that from the point \(C\) lying outside of the circle we can draw exactly two tangents to the circle and the lengths of these tangents (that is, the distance from \(C\) to the points of tangency) are equal.
Two circles intersect at points \(A\) and \(B\). Point \(X\) lies on the line \(AB\), but not on the segment \(AB\). Prove that the lengths of all of the tangents drawn from \(X\) to the circles are equal.
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 \(d^2 = R_1^2 + R_2^2\).