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 Figure).
Solution:
O is the centre of two concentric circles. We need to prove that AB=CD.
Construction: Let’s draw
We can note that BC is the chord of smaller circle and OM is the perpendicular to it.
(1)
(Perpendicular from the centre of the circle to a chord bisects the chord)
Similarly, we have chord AD of bigger circle and OM is the perpendicular to it.
(2)
(Perpendicular from the centre of the circle to a chord bisects the chord)
Subtracting (1) and (2), we get
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