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Question

In fig 4.41 chord AB || chord CD of a circle with centre O and radius 5 cm such that AB = 6cm and CD = 8cm, if OP AB, OQ CD, Determine PQ.

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Solution



Join OA and OC.Radius = 5 cmOA= OC= 5 cmWe know that perpendicular from the centre of a circle on a chord bisects the chord.AP = BP = AB2=62=3 cmAnd CQ= DQ = CD2=82=4 cmIn right OAP,OP = OA2 - AP2 =52 -32 =25-9 =16 =4 cmAnd in right OCQ,OQ = OC2 -CQ2 =52 -42 =25-16 =9 =3 cmFrom the figure,PQ = OP - OQ = 4 cm - 3 cm = 1 cm PQ = 1 cm

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