Q26. There are two concentric circles with centre OAD is a chord of a

1.	Q26. There are two concentric circles with centre OAD is a chord of a larger circle intersecting the smallercircle at B and C Prove that AB-CD
Answer» Let AD and BC be the chords of bigger and smaller circles. By the definition of segments, we have AP = AB + BP ....(1) and PD = CP + CD....(2) Let OP be the perpendicular line to the chords. Since the perpendicular line to the chord bisects the chord, OP bisects the chord AD and OP bisects the chord BC. Thus, AP = PD...(3) and BP = CP...(4) In equations (1) and (2), use AP = PD AB + BP = CP + CD Since BP = CP, we have AB = CD

Q26. There are two concentric circles with centre OAD is a chord of a larger circle intersecting the smallercircle at B and C Prove that AB-CD

Answer»

Let AD and BC be the chords of bigger and smaller circles.

By the definition of segments, we have

AP = AB + BP ....(1)

and

PD = CP + CD....(2)

Let OP be the perpendicular line to the chords.

Since the perpendicular line to the chord bisects the chord,

OP bisects the chord AD and OP bisects the chord BC.

Thus,

AP = PD...(3)

and

BP = CP...(4)

In equations (1) and (2), use AP = PD

AB + BP = CP + CD

Since BP = CP, we have

AB = CD