Question
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.
✓
Answer
Given: A line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D.
To prove : AB = CD
Construction : Draw $O M \perp B C$
Proof: $\because$ The perpendicular drawn from the centre of a circle to a chord bisects the chord.
$\therefore$ AM = DM
and BM = CM
Subtracting (2) from (1), we get
AM - BM = DM - CM
$\Rightarrow$ AB = CD
To prove : AB = CD
Construction : Draw $O M \perp B C$
Proof: $\because$ The perpendicular drawn from the centre of a circle to a chord bisects the chord.
$\therefore$ AM = DM
and BM = CM
Subtracting (2) from (1), we get
AM - BM = DM - CM
$\Rightarrow$ AB = CD
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