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Question

# In the diagram, AB is the diameter of a circle with centre O. PQ is a chord perpendicular to AB. N is the point of intersection of AB and PQ and ON=5cm. If the radius of the circle is 13 cm the length of chord PB, in cm, is

A
12
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B
413
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C
213
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D
14
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Solution

## The correct option is C 4√13Solution:Given that:OA=OB=OP=13cm,ON=5cmTo find:PB=?Solution:BN=OB−ON=13cm−5cm=8cmIn △PNOOP2=ON2+PN2 (By Pythagorus theorem)or, 132=52+PN2or, PN2=169−25=144cm2or, PN=12cmNow, In △PBNPB2=PN2+BN2 (By Pythagorus theorem)or, PB2=122+82or, PB2=144+64=208cm2or, PB=4√13cmHence, B is the correct option.

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