Q. 134.2( 5 Votes )

# If the angle-bisector of two intersecting chords of a circle passes through its centre, then let me prove that the two chords are equal.

Answer :

Given, OF is angle bisector of AFC.

**Construction:** OQ ⊥ AB and OP ⊥ CD

In ΔOFQ and ΔOFP

∠OFQ = ∠OFP (given)

OF = OF(Common)

∠OQF = ∠OPF(Construction)

AAS Congruency.

ΔOPR ≅ΔOPQ.

∴ OR = OQ (C.P.C.T)

Hence AB = CD

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