Question

O is centre of the circle. Find the
length of radius, if the chord of
length 24 cm is at a distance of 9 cm
from the centre of the circle.
2m​

Answer 1

Answer:

radius = 15

here as shown

you can use Pythagoras theorem

here I have assumed half of chord which is 12

distance between centre and chord which is 9

and we have to find OB which is not known

so use Pythagoras

where,

square of hypotenuse = square of base + sq. of height

Answer 2

Given:

✰ O is centre of the circle.

✰ Length of the chord = 24 cm

✰ Distance from the centre of the circle = 9 cm

To find:

✠ The radius of a circle.

Solution:

O is centre of the circle.

Let OA be the radius of a circle and AB be the chord of length 24 cm.Let the perpendicular drawn from the center of circle O to the chord AB be C.

OC ⟂ AB

We know that the perpendicular drawn from the center of circle C bisects the chord into two parts, so,

➛ AC = CB = 1/2 AB

➛ AC = CB = 1/2 × 24

➛ AC = CB = 24/2

➛ AC = CB = 12 cm

∆OCB is the right angled triangle at C.

By using Pythagoras theorem,

➤ OA² = OC² + AC²

➤ OA² = 9² + 12²

➤ OA² = 81 + 144

➤ OA² = 225

➤ OA = √225

➤ OA = 15 cm

∴ The radius of a circle = 15 cm

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