A circle has a radius of 15 cm. A chord is drawn. The distance from the centre of the circle Class 9
R
RBSEGuide
A circle has a radius of 15 cm. A chord is drawn. The distance from the centre of the circle Class 9
Question 1.
A circle has a radius of 15 cm. A chord is drawn. The distance from the centre of the circle to the chord is 9 cm. What is the length of the chord? Class 9
Solution:
Radius of circle = OA = 15 cm
Distance of chord from centre = OM = 9 cm
In right-angled ∆OMA
OA² = OM² + MA²
...[By Baudhayana-Pythagoras theorem]
∴ 15² = 9² + MA²
∴ MA² = 225 - 81
∴ MA² = 144
∴ MA = 12 cm
Since the perpendicular from the centre of a circle to a chord bisects the chord.
∴ AB = 2 × MA = 2 × 12 = 24 cm
∴ The length of the chord is 24 cm.