If in a circle a chord of length 14 cm is at a distance of 24 cm from its center, then the length of the radius of the circle is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 25 cm.
AB = 14 cm and OM = 24 cm
Here, OM ⊥ AB
The perpendicular from the center of a circle to a chord bisects the chord.
So, AM = MB = AB/2 = 7 cm (radius)
△OAM is a right-angle triangle.
So, OA2 = OM2 + AM2
⇒ OA2 = 242 + 72 = 576 + 49 = 625
⇒ OA = √625 = 25
Therefore, the length of the radius of the circle is 25 cm.