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If a line intersects two concenteric cir...

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

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Let OP be the perpendicular from O on line l. since, the perpendicular from the centre of a circle to a chord bisects the chords.
Now, BC is the chord of the smaller circle and `OP botBC` .
`thereforeAP=PC`......(1)
Since, AD is a chord of the larger circle and `OPbotAD`
`therefore AP=PD` ......(2)
On subtracting eq. (1) from eq. (2), we get
`AP-BP=PDrArrAB=CD`
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