Question

In the given diagram, O is the centre of the circle and chord AB = chord BC.
(i) What is the relation between arc AB and arc BC?
(ii) What is the relation between $\angle AOB$ and $\angle BOC$? [1 Mark]

Answer 1

Concept: 0.5 Mark each

(i) Since equal chords in a circle cut equal arcs, so

$chordAB=ChordBC$

$\to arcAB=arcBC$.

(ii) Equal arcs in a circle make equal angles at the centre.

$ChordAB=ChordBC$

$\to arcAB=arcBC$

$\to \angle AOB=\angle BOC$