Question

Fill In The Blanks

If two equals chords AB and AC of a circle with centre O are on the opposite sides of OA, then ∠OAB = ____________ .

Answer 1

Given:
AB =AC
AB and AC lies on the opposite sides of OA


The chords of equal length, are equidistant from 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.)

Hence, ∠OAB = ∠OAC.