Mathematics
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.
Circles
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Answer
Draw a perpendicular from the center of the circle to the line AD, such that OM ⊥ AD
BC and AD are the chords of smaller circle and the bigger circle respectively.
We know that,
Perpendicular from the center bisects the chord.
⇒ BM = MC ……… (1)
⇒ AM = MD ……… (2)
By subtracting equation (1) from (2), we get :
⇒ AM − BM = MD − MC
⇒ AB = CD
Hence, proved that AB = CD.
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