Question

$AB$ is a diameter of a circle and $PT$ is a tangent to the circle.If $PB=2$cm,$PT=8$cm,calculate the radius of the circle.

Answer 1

$PT$ is a tangent and $ABP$ is a secant to the circle.

$\Rightarrow PA\times PB={PT}^2$

$\Rightarrow PA\times 2=8^2$

$\Rightarrow PA=\frac{64}{2}=32$cm

But $PA=AB+BP$

$\Rightarrow AB=32-2=30$cm

Hence, radius of the circle$=\frac{1}{2}\left(AB\right)$

$=\frac{1}{2}\times 30=15$cm