Q.Two circles intersect each other. The radius of each circle is 10 cm. The length of the common chord is 16 cm. Find the distance between the centers of the two circles.

Two circles centered at A and B, each with a radius of 10 cm, intersect at points P and Q. PQ = 16 cm AB intersects PQ at point O. \(\therefore\) In triangle AOP, AP = 10 cm OP = \(\frac{PQ}{2} = \frac{16}{2}\) cm = 8 cm \(\therefore\) AO = \(\sqrt{AP^2 - OP^2} = \sqrt{10^2 - 8^2}\) cm \(= \sqrt{100 - 64} = \sqrt{36} = 6\) cm \(\therefore\) AB = 2AO = \(2 \times 6\) cm = 12 cm \(\therefore\) The distance between the centers of the two circles is 12 cm.
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