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A Line through the Center That Bisects the Chord Is Perpendicular to the Chord

In the given ...

Question

In the given figure O is the centre of the circle with radius 10 cm. OP and OQ are perpendiculars to AB and CD respectively. Determine the value of PQ if AB = 16 cm and CD = 12 cm.

10cm

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12cm

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13cm

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14cm

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Solution

The correct option is D 14cm
Given, AB = 16 cm.
$⟹$ PB= 8 cm
( $∵$ The perpendicular from the center to a chord bisects the chord)
Similarly, CQ = 6 cm.
Also, given that radius of the circle is 10 cm and OP and OQ are perpendiculars to AB and CD respectively.
$Δ$ APO and $Δ$ CQO form right angled triangle.
By applying Pythagorus theorem for these triangles, we get
PO = 6 cm and QO = 8 cm.
PQ = PO + QO = 6 + 8 = 14 cm

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