Question

A, B and C are three points on the circle whose centre is O. If $\angle BAC=x,\angle CBO=\angle BCO=y,\angle BOC=t$, reflex $\angle BOC=z$, then

• A. $x-y={90}^o$
• B. $x+y={90}^o$
• C. $t+2y^o={90}^o$
• D. None of these

Answer 1

The correct option is A $x-y={90}^o$

$\angle x=\frac{z}{2}$ (Angle made by arc at the centre is double the angle made by arc in the alternate segment)
$\angle z=2\angle x$
$\angle t=360-\angle z$
$=360-2\angle x$
In $\Delta$ BOC
$\angle t+\angle y+\angle y={180}^o$
$\angle t+2\angle y={180}^o$
${360}^o-2\angle x+2\angle y={180}^o$
$x-y={90}^o$