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. $12$
• B. $4\sqrt{13}$
• C. $2\sqrt{13}$
• D. $14$

Answer 1

Answer: (B)

$4\sqrt{13}$

Solution:

Given that:

$OA=OB=OP=13cm,ON=5cm$

To find:

$PB=?$

Solution:

$BN=OB-ON=13cm-5cm=8cm$

In $△PNO$

$O{P}^2=O{N}^2+P{N}^2$ (By Pythagorus theorem)

or, ${13}^2=5^2+P{N}^2$

or, $P{N}^2=169-25=144c{m}^2$

or, $PN=12cm$

Now, In $△PBN$

$P{B}^2=P{N}^2+B{N}^2$ (By Pythagorus theorem)

or, $P{B}^2={12}^2+8^2$

or, $P{B}^2=144+64=208c{m}^2$

or, $PB=4\sqrt{13}cm$

Hence, B is the correct option.