Question

In the adjoining figure, AB and AC are two equal chords of a circle with centre O. Show that O lies on the bisector of $\angle BAC$. [3 MARKS]

Answer 1

Similarity of Triangles: 2 Marks
Answer: 1 Mark

AB and AC are equal chords of a circle with centre O and O has been joined with A.

To prove : $\angle BAO=\angle CAO$.


Proof:

In $\Delta OAB$ and $\Delta OAC$, we have

(i) AB = AC (Given)

(ii) OB = OC (Radii of the same circle)

(iii) OA = OA (Common side)

$\therefore$ $\Delta OAB\cong \Delta OAC$ (By SSS congruency criterion)

Hence, $\angle BAO=\angle CAO$ (By C.P.C.T)

Hence the centre of the circle lies on the bisector of $\angle BAC$.