Question

Hello guys!!☺♡

•A line 'l' is intersecting two concentric circles having a common centre 'O',at A,B,C and D.Prove that AB=CD.
(With diagram plzz)

Ques. frm chp:CIRCLES
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Answer 1

HEY MATE.....
THIS IS YOUR 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

HOPE IT IS HELPFUL......
GOT IT......

Answer 2

Draw OM⊥ l
Since perpendicular from the centre of a circle to a chord of the circle bisects the chord.
BM = CM …(i)
and AM = DM …(ii)
Subtracting (i) from (ii), we have
AM – BM = DM – CM
AB = CD