Question

Fill In The Blanks

If AB and AC are equal chords of a circle, then the biesector of ∠BAC passes through the ___________.

Answer 1

Given:
AB and AC are equal chords of a circle


Let O be the centre of the circle.

In ∆OAB and ∆OAC,
AB = AC (given)
OA = OA (common)
OB = OC (radius of the circle)

By SSS property,
∆OAB ≅ ∆OAC

Therefore, ∠OAB = ∠OAC (by C.P.C.T.)

Thus, ∠BAC = 2∠OAB.

Hence, the bisector of ∠BAC passes through the centre.