Question

Two concentric circles with center O are cut by a line at A,B,C and D, prove that AB=CD

please answer me

Answer 1

Circles having same Centre are called concentric circles.

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

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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.

OM ⊥ AD is drawn from O.

OM bisects AD as OM ⊥ AD.


 AM = MD
— (i)

 

Here, BC is the chord of the smaller circle.



OM bisects BC as OM ⊥ BC.



BM = MC — (ii)



From (i) and (ii),

On subtracting eq i from eq ii



AM – BM = MD – MC


AB = CD    

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Hope this will help you....

Answer 2

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