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Suppose the lengths of the tangents drawn from A(x1, y1) and B(x2, y2) to the circle x2 + y2 = a^2 are of lengths

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Suppose the lengths of the tangents drawn from A(x1, y1) and B(x2, y2) to the circle x2 + y2 = a2 are of lengths l1 and l2, respectively, and x1x2 + y1y2 = a2. Then show that (AB)2 is equal to l12 + l22.

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We have

Therefore

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