Question

In fig. P is the centre of the circle. Prove that :
$\angle XPZ=2(\angle XZY+\angle YXZ)$

Answer 1

$m=\frac{\gamma }{2}$ (prperty of a circle)
$Now\frac{\gamma }{2}+\angle 3={180}^{\circ }$
$\angle 3={180}^{\circ }-\frac{\gamma }{2}------\left(1\right)$
$also\Delta XYZ$
$\alpha +\beta +\angle 3={180}^{\circ }$
$\angle 3={180}^{\circ }-\left(\alpha +\beta \right)$
From equation 1
$\angle XPZ=2(\angle XZY+\angle YXZ)$