06/19/2020 (2011: Countdown Round, Problem 19)

Q: Circle O has a diameter of 24 cm. Chord CD is the perpendicular bisector of segment OA. What is the length of chord CD, in cm? Express your answer in simplest radical form.

A: 6√(3)

If the diameter is 24, that means the radius is 24/2 = 12. AO  is a radius, so its length is 12.

Because CD bisects it, that means that the distance between the intersection of CD & AO and O is 6.

CO is a radius, so that means that its length is 12.

Using the Pythagorean Theorem, we find that the distance between the intersection of CD & AO and C is 3√(3).

That is 1/2 of the length of CD, so CD = 3√(3) * 2 = 6√(3).