A circle with centre O has radius 15 cm. D is a point on the circle such that a 24 cm long chord AB is bisected by OD at point C. Find the length of CD (in cm).
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 6
Calculations:
We know that if the radius of the circle is perpendicular to the chord, it bisects the chord in two equal parts.
In triangle OAC, using pythagoras theorem
AC2 + OC2 = OA2
OC2 = 152 - 122 = 225 - 144 = 81
OC = 9
We know that, CD = OD - OC
OD = radius of the circle = 15 cm
CD = 15 - 9 = 6 cm