Mathematics
If a line l intersects two concentric circles at the points A, B, C and D, as shown in the figure, prove that AB = CD.
Answer
Since, the perpendicular to a chord from the centre of the circle bisects the chord,
So, in the smaller circle, L is mid-point of BC so,
BL = LC = x (let)
Similarly, in larger circle L is mid-point of AD so,
AL = LD = y (let)
From figure,
AB = AL - BL = (y - x)
CD = LD - LC = (y - x)
∴ AB = CD.
Hence, proved that AB = CD.
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