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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 $$ON = 5 cm$$. If the radius of the circle is 13 cm the length of chord PB, in cm, is
426873_cc9e453a300c41a9b412f4115e795c6a.png


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 $$4\sqrt{13}$$
Solution:
Given that:
$$OA=OB=OP=13cm, ON=5cm$$
To find:
$$PB=?$$
Solution:
$$BN=OB-ON=13cm-5cm=8cm$$
In $$\triangle PNO$$
$$OP^2=ON^2+PN^2$$     (By Pythagorus theorem)
or, $$13^2=5^2+PN^2$$
or, $$PN^2=169-25=144cm^2$$
or, $$PN=12cm$$
Now, In $$\triangle PBN$$
$$PB^2=PN^2+BN^2$$     (By Pythagorus theorem)
or, $$PB^2=12^2+8^2$$
or, $$PB^2=144+64=208cm^2$$
or, $$PB=4\sqrt{13}cm$$
Hence, B is the correct option.

Mathematics

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