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

A
12
B
413
C
213
D
14

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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