Question

The length of chord AB in circle O is 24. Vanessa said that any chord of circle O that inter- sects AB at its midpoint, M, is separated by M into two segments such that the product of the lengths of the segments is 144. Do you agree with Vanessa? Justify your answer.

Answer 1

If two chords intersect each other inside a circle, the products of their segments are equal.

If M is midpoint of AB, then AM = MB = 24/2 = 12.

Product of the lengths of the segments AM and MB:
AM * MB = 12 * 12 = 144

So, any chord of circle O that intersects AB at its midpoint, M, wll be separated by M into two segments such that the product of the lengths of the segments is 144.