[Figure: a circle with centre O. Points A, B, C lie on the circle, B at the top and A, C lower down; chords AB and BC are drawn; X is a point on the arc AXC below, and the rays from A and from C through X are produced beyond X, outside the circle.]In…

Q.2 (A)(1)

[Figure: a circle with centre O. Points A, B, C lie on the circle, B at the top and A, C lower down; chords AB and BC are drawn; X is a point on the arc AXC below, and the rays from A and from C through X are produced beyond X, outside the circle.]

In the above figure, ∠ABC is inscribed in arc ABC.

If ∠ABC = 60º, find m∠AOC.

Solution :

∠ABC = \(\dfrac{1}{2}\) m(arc AXC) ............ ____

60º = \(\dfrac{1}{2}\) m(arc AXC)

____ = m(arc AXC)

But m∠AOC = m(arc .....) ............ (Property of central angle)

∴ m∠AOC = ____