Q6 of 29 Page 61

In the figure at right, AB and CD are two parallel chords of a circle with centre O and radius 5 cm such that AB = 6 cm and CD = 8 cm. If OP ⊥ AB and CD ⊥ OQ determine the length of PQ.

From Theorem: A circle with radius r and a chord of length l which is at distance d from the centre, follows the equation,



For Triangle COQ


OC = 5cm ,


CQ = half of chord length = 4cm


From Pythagoras theorem




OQ = 3cm


For triangle POA


OA = 5cm, AP = half of chord length = 3cm


From Pythagoras theorem




OP = 4cm


From figure PQ = OP – OQ


Therefore PQ = 1cm




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In the figure at right, AB and CD are two parallel chords of a circle with centre O and radius 5 cm. Such that AB = 8 cm and CD = 6 cm. If OP ⊥ AB and OQ ⊥ CD determine the length PQ.