Question

If a lines intersects two concentric circles (circles with the same centre) which centre O at A,B,C and D. prove that AB = CD .​

Answer 1

Answer:

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Answer 2

Answer:

Circles having same Centre are called concentric circles.

The perpendicular from the centre of a circle to a chord bisects the chord.

Let a line intersects two concentric circles with Centre O at A, B, C and D.

To Prove:

AB=CD

Construction:

Draw OM perpendicular from O on a line.

Proof:

We know that the perpendicular drawn from the centre of a circle to a chord bisects the chord.

Here,AD is a chord of a larger circle.

OMLAD is drawn from O.

OM bisects AD as OM L AD.

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AM = MD - (1)

Here, BC is the chord of the smaller circle.

OM bisects BC as OM L BC.

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V

BM = MC - (ii)

From (i) and (ii),

On subtracting eq i from eq ii

AM - BM = MD - MC

AB = CD

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Step-by-step explanation:

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