Question

C is a point on the minor arc AB of the circle, with the centre O. Given $\angle$ ACB = $x^{\circ }$ and $\angle$ AOB = $y^{\circ }$ .Express y in terms of x. Calculate x, if ACBO is a parallelogarm.

Answer 1

Clearly, major arc BA subtends $x^{\circ }$ at a point on the remaining part of the circle.

Reflex $\angle$AOB = $2x^{\circ }$
${360}^{\circ }$ - $y^{\circ }$ = $2x^{\circ }$
$y^{\circ }$ = ${360}^{\circ }$ - $2x^{\circ }$

Since ACBO is a parallelogram.

$\therefore$ $x^{\circ }$ = $y^{\circ }$ i.e. x = y
x = ${360}^{\circ }$ -2x
3x = ${360}^{\circ }$
x = ${120}^{\circ }$