# 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. 10.25).

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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. 10.25).

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Draw OL_|_AD
AD is a chord of outer circle.
AL=LD-(1)
BC is a chord of inner circle.
BL=LC-(2)
Subtracting equation 1 from 2
AL-BL=LD-LC
AB=CD.