Problema Solution
A line cuts two concentric circles at A, B, C and D. Prove that AB = CD
Answer provided by our tutors
Use the theorem: The perpendicular from the center of a circle to a chord bisects the chord.
Lets denote with O the center of the circles.
Take the perpendicular to AD passing through O and crossing at P.
By symmetry, it must be true that PB and PC are equal.
Similarly, PA and PD must be equal.
Therefore, PA-PB=AB equals PD-PC=CD.