if PQ and RS be tangents at the extrimities of diameter PR of a circle of radius r . if PS and RQ intersect at a point X on the circumference of the circle, then 2r equals

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if PQ and RS be tangents at the extrimities of diameter PR of a circle of radius r . if PS and RQ intersect at a point X on the circumference of the circle, then 2r equals

in triangle PRS

tan(90-@) = RS/2r => cot@ = RS/2r  ...... eq. 1

in triangle PQR

tan@ = PQ/2r ...... eq. 2

from the above eq. 1 and 2

(2r)² = RS.PQ