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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.


A
10cm
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B
12cm
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C
13cm
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D
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.
ΔAPO and ΔCQO 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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