Question

In the figure given below, $O$ is the centre of the circle and $SP$ is a tangent. If $\angle SRT={65}^o$, find the value of $x$, $y$ and $z$.

Answer 1

In $△OSP$, $\angle OSR={90}^o$ [Radius is perpendicular to tangent]
In $△TSR$
$x+{90}^o+{65}^o={180}^o$
$\therefore$ $x={25}^o$
$\angle SOQ=2\angle STR$
[Angle at centre $=2\times$ Angle at circumference]
$y=2\times 25={50}^o$
In $△OSP$,
${50}^o+{90}^o+z={180}^o$
$\therefore$ $z={40}^o$