Question

In the following figure if O is the centre of the circle, AC = 5 cm and BC = 12 cm, then the radius of the circle is

Answer 1

Given AB is the diameter of the circle.
$\angle ACB={90}^{\circ }$ [Angle in a semicircle]

Applying Pythagoras theorem in $△ABC$,
$A{B}^2=A{C}^2+B{C}^2$
$\Rightarrow A{B}^2=5^2+{12}^2$
$\Rightarrow A{B}^2=169$

$\therefore AB=13cm$

$\Rightarrow$ radius $=\frac{13}{2}=6.5cm$

Therefore, the radius of the circle is $6.5cm$