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Question

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


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Solution

Solve for the required proof:

Draw a perpendicular OM from O.

As perpendicular from center of circle to the chord bisects the chord.

So, in inner circle, BM=MC ...i

And for outer circle, AM=MD ...ii

Now subtract i from ii, we get;

AM-BM=MD-MC

AB=CD

Hence proved.


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