Q13 of 31 Page 65

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.


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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