Q9 of 141 Page 400

In the given figure, is the center of a circle in which chords and intersect at such that bisects Prove that

Proof


In ΔOEP and ΔOFP,


∠OEP = ∠OFP [equal to 90°]


OP = OP [common]


∠OPE = ∠OPF [OP bisects ∠BPD]


Therefore,


ΔOEP = ΔOFP [By angle-side-angle]


∴ OE = OF


AB = CD [Chords are equidistant from the center]


Hence, AB = CD Proved.


More from this chapter

All 141 →
7

In the given figure, a circle with center is given in which a diameter bisects the chord at a point such that and Find the radius of the circle.

 8

In the adjoining figure, is perpendicular to the chord of a circle with center If is a diameter, show that and

10

Prove that the diameter of a circle perpendicular to one of the two parallel chords of a circle is perpendicular to the other and bisects it.

 11

Prove that two different circles cannot intersect each other at more than two points.