Question

In the given figure, Find the distance of a chord of length 16 cm from the centre of a circle of radius 10 cm. ​

Answer 1

The length of the chord = 16cm

The length of the chord = 16cmThe radius of the circle = 10cm

When a perpendicular is drawn on the chord such that the chord is bisecting into two. Then the length of the chord will be halved, that is it becomes 8cm.

Using the Pythagorean theorem,

OA^2 = OC^2 + AC^2

OA^2 = OC^2 + AC^210^2 = OC^2 + 8^2

OA^2 = OC^2 + AC^210^2 = OC^2 + 8^2100 = OC^2 + 64

OA^2 = OC^2 + AC^210^2 = OC^2 + 8^2100 = OC^2 + 64OC^2 = 36

OA^2 = OC^2 + AC^210^2 = OC^2 + 8^2100 = OC^2 + 64OC^2 = 36OC = 6cm

Therefore, the distance of the chord from the centre of the circle is 6cm.