Question

Consider the given figure. P is the centre of the circle.

The radius of the circle is units

Answer 1

The given figure is as follows:

The side XY passes through the center of the circle and touches the circle at both ends.
Hence, it is the diameter of the circle.

The angle subtended by the diameter to any point on the circle is equal to ${90}^o.$
$\therefore \angle Z={90}^o,$ and the given triangle is a right triangle.

Also, XY is the hypotenuse of the given triangle.
Hence, $XY=\sqrt{3^2+4^2}=\sqrt{25}=5\text{units}$

$\therefore$ Radius of the triangle is $\frac{XY}{2}=\frac{5}{2}=2.5\text{units}.$