Q14 of 141 Page 400

If a diameter of a circle bisects each of the two chords of a circle then prove that the chords are parallel.

Let AB and CD are two chords of a circle with center O.


Diameter POQ bisect s them at L and M.



Then,


OLAB and OMCD


∴ ∠ALM = ∠LMD


∴ AB||CD [Alternate angles]


More from this chapter

All 141 →
12

Two circles of radii 10 cm and 8 cm intersect each other, and the length of the common chord is 12 cm. Find the distance between their centers.

 13

Two equal circles intersect in and A straight line through meets the circles in and Prove that

15

In the adjoining figure, two circles with centers at and and of radii 5 cm and 3 cm touch each other internally. If the perpendicular bisector of meets the bigger circle in and find the length of

16

In the given figure, is a chord of a circle with center and is produced to such that Also, is joined and produced to meet the circle in If and prove that