A chord AB of a circle is 30 cm long. If the perpendicular distance from the center to AB is 12 cm, calculate the radius of the circle. Also, determine the distance of another chord of length 24 cm from the center.
Show answer & explanation
Correct answer: A
Explanation
Given:
Chord AB = 30 cm, Distance from the center = 12 cm
Second chord = 24 cm
According to the formula:
r² = d² + (l/2)²
r² = 12² + (30/2)²
= 144 + 225 = 369
r = √369 = 19.2
For the second chord:
d² = r² − (24/2)²
= 369 − 12²
= 369 − 144 = 225
d = 15
Radius = 19.2 cm, Distance = 15 cm