Find the length of the chord of a circle where the radius is 7cm and perpendicular distance is 6 cm. Class 9

Find the length of the chord of a circle where the radius is 7cm and perpendicular distance is 6 cm. Class 9

Question 1.

Find the length of the chord of a circle where the radius is 7cm and perpendicular distance is 6 cm. Class 9

Solution:

Let O be the centre of the circle with radius = OA = 7 cm

Let OM be the perpendicular drawn from O to chord AB.

∴ OM = 6 cm

To find: length of chord AB

The perpendicular from the centre to a chord bisects the chord.

∴ AM = MB = $\frac{\mathrm{AB}}{2}$

In right-angled ∆OMA,

OA² = OM² + AM² ...[By Baudhayana-Pythagoras theorem]

∴ 7² = 6² + AM²

∴ 49 = 36 +AM²

∴ AM² = 13

∴ AM = $\sqrt{13}$

AB = 2 × AM

∴ AB = 2$\sqrt{13}$ cm

∴ Length of the chord = 2$\sqrt{13}$ cm