Question

In a circle with centre 0. chord of a circle is 30cm long, its distance from the center
is 8cm. Find the radius of the circle?
(1) 17 cm
(2) 15 cm
(3): 16 cm
(4) 12 cm​

Answer 1

Answer:

16 cm long

Step-by-step explanation:

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Answer 2

Given:

✰ Length of chord of a circle = 30 cm

✰ The distance from the center = 8 cm

To find:

✠ The radius of the circle.

Solution:

Let AB be the chord of a circle of length 30 cm, and

OC be the distance from the center to the chord AB is 8 cm

➛ AB = 30 cm

➛ AC + CB = 30

➛ AC + AC = 30 [ ∵ Perpendicular drawn from the centre of the circle bisects the chord into two parts ( AC and CB ). These parts are the radius of the circle. Therefore, CB = AC ]

➛ 2AC = 30

➛ AC = 30/2

➛ AC = 15 cm

In ∆ACO,

➛ ∠C = 90°

➛ OA² = AC² + OC²

➛ OA² = 15² + 8²

➛ OA² = 225 + 64

➛ OA² = 289

➛ OA = √289

➛ OA = 17 cm

∴ The radius of the circle = 17 cm

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