Question

In Fig. 16.202, O is the centre of the circle such that ∠AOC=130°, then ∠ABC=
A. 130°
B. 115°
C. 65°
D. 165°

Answer 1

In Fig. 16.202, O is the centre of the circle such that ∠AOC=130°, then

∠ ABC =  115°

Option B is correct.

Given,

O is the centre of the circle

∠ AOC = 130°

As we know that, the angle subtended by  a chord at the centre is twice that of subtended at any part of the circle.

∴ ∠ APC = ∠ AOC /2 = 130°/2 = 65°

From figure it's clear that, APBC is a cyclic quadrilateral, we have,

∠ ABC + ∠ APC = 180° ( vertically opposite angles are equal)

∠ ABC + 65° = 180°

∠ ABC = 180° - 65°

∴ ∠ ABC = 115°