Question

Two concentric circles of radii $13cm$ and $5cm$ are drawn. Find the length of the chord of the outer circle which touches the inner circle.

Answer 1

In the above shown figure, $OP\perp AB,$ $OA=13$ cm and $OP=5$ cm

$AP=PB.......\left(1\right)$

Consider $△APO$ and apply pythagoras theorem as follows:

$A{P}^2+O{P}^2=O{A}^2\Rightarrow A{P}^2+5^2={13}^2\Rightarrow A{P}^2+25=169\Rightarrow A{P}^2=169-25\Rightarrow A{P}^2=144\Rightarrow AP=\sqrt{144}\Rightarrow AP=12=PB\left(From\right(1\left)\right)$

Therefore, $AB=AP+PB=12+12=24$ cm

Hence, the length of the chord $AB$ is $24$ cm.