Question

A chord ab of a circle with centre o is 10 cm. If the chord is 12 cm away from centre, then what is the radius of the circle

Answer 1

Given,

A circle with centre O.

Chord, AB = 10 cm

Distance of tbe chore from the centre = 12 cm

To find,

The radius of the circle.

Solution,

The radius of the circle will be 13 cm.

We can easily solve this problem by following the given steps.

Now, first, draw a perpendicular line from the centre of the circle on the chord. Let's take this point to be C.

Join OA (radius).

( OA and OB will be equal as they are the radii of the circle.)

Then, AC = CB = AB/2

AC = CB = 10/2 cm

AC = CB = 5 cm

According to the question,

OC = 12 cm

∆ OCA is a right-angled triangle.

Using the Pythagoras theorem in ∆ OCA,

OA² = OC² + AC²

OA² = (12)² + (5)²

OA² = 144 + 25

OA² = 169

OA = √169

OA = 13 cm

Hence, the radius of the circle is 13 cm.