in the given figure,O is the center of the circle with radius 5cm.OP is perpendicular to AB,OQ is perpendicular to CD,AB=6cm and CD=8cm. determine PQ.

We have, O as the centre of circle whose radius is 5 cm.AB and CD are two chord of a circle.AB = 6 cm; CD = 8 cm; OA = OD = 5 cmAlso, OPAB and OQCD.We know that  drawn from the centre to the chord bisects the chord.So, AP = PB = AB2 = 3 cmand CQ = QD = CD2 = 4 cmIn OPA,      OP2 = OA2 - AP2  Pythagoras theoremOP2 = 52-32OP2 = 25 - 9OP2 = 16OP = 4 cmIn OQD,    OQ2 = OD2-QD2  Pythagoras theoremOQ2 = 52-42OQ2 = 25 - 16OQ2 = 9OQ = 3 cmNow, PQ = OP + OQ = 4 + 3 = 7 cm

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Use the Pythagoras theorem on both the right angled triangles
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