The distance of a chord of length 16 cm from the centre of a circle is 6 cm. Find the radius of the circle. Class 9
R
RBSEGuide
The distance of a chord of length 16 cm from the centre of a circle is 6 cm. Find the radius of the circle. Class 9
Question 1.
The distance of a chord of length 16 cm from the centre of a circle is 6 cm. Find the radius of the circle. Class 9
Solution:
Length of chord = AB = 16 cm
Distance of chord from centre = OM = 6 cm
Since the perpendicular from the centre of a circle to a chord bisects the chord.
∴ MA = $\frac{16}{2}$ = 8 cm
In right-angled ∆OMA
OA² = OM² + MA²
...[By Baudhayana-Pythagoras theorem]
∴ OA² = 6² + 8²
∴ OA² = 36 + 64
∴ OA² = 100
∴ OA = 10 cm
∴ The radius of the circle is 10 cm.