A chord of a circle is at a distance of 9 cm from the center, and its length is 24 cm. Find the radius of the circle. Also, calculate the distance of another chord of length 18 cm from the center.
Show answer & explanation
Correct answer: C
Explanation
Given:
Chord₁ = 24 cm, Distance₁ = 9 cm
According to the formula:
r² = (Chord/2)² + Distance²
r² = (24/2)² + 9² = 12² + 9² = 144 + 81 = 225
r = 15 cm
Now, Chord₂ = 18 cm
Distance² = r² − (Chord/2)²
= 225 − (18/2)²
= 225 − 9²
= 225 − 81 = 144
Distance = 12 cm
The radius is 15 cm, and the distance of the second chord is 12 cm.