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Let A be one point of intersection of two intersecting circles with centres O and Q. The tangents at A to the two circles meet the circles again at B and C respectively. Let the point P be located so that AOPQ is a parallelogram. Prove that P is the circumcentre of the triangle ABC.

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Answer is ......

Thus, P is the point of intersection of perpendicular bisectors PQ and PO of sides AC and AB respectively.
Hence, P is the circumcentre of ΔABC.

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