Question

In the given figure, O is the centre of the circle. Find the value of x.

Answer 1

Take triangle DCB, we have
DB is a diameter so, $\angle BCD={90}^{\circ }$ {Angle in a semicircle}
Consider $\Delta BCD,$ we have
$\angle BCD={90}^{\circ },\angle BDC=2x$ and $\angle DBC=?$
$\angle DBC={180}^{\circ }-[{90}^{\circ }+2x]$ {sum of all angles of a triangle is 180}
$={90}^{\circ }-2x$
$\angle DAC=\angle DBC$ [angle formed on same segment]
$\Rightarrow x={90}^{\circ }-2x$
$\Rightarrow 3x={90}^{\circ }$
$\Rightarrow x={30}^{\circ }$