Question

a chord of a circle is 20 cm in length and its distance from the centre is 24cm find the radius of the circle​

Answer 1

Answer:

Here, AB = 20cm and OC = 24cm

Now,

AC=CB=

2

AB

=10cm (perpendicular drawn from centre of the circle to the chord,bisects the chord)

Then using Pythagorean Theorem:

OA=

(AC

2

+OC

2

)

=

(10

2

+24

2

)

=

676

=26

Answer 2

Answer:

26cm

Step-by-step explanation:

Given,

• Chord of the circle,c = 20cm
• Distance from center to chord = 24cm

To find,

• Radius,r of the circle = ?

We can solve this easily using the Pythagorean formula :-

• ab²+bc² = ac²
• base square + height square = hypotenuse square
• Here, hypotenuse is RADIUS of the circle.

We know that,

• chord is divided into two equal parts by the line from center whose Length is 24cm. So,
• Height,ab = 24cm and chord/2 = 20/2 = bc = 10cm

Now, substitute the values in the formulae :-

• ab² + bc² = ac²
• 24² + 10² = ac²
• ac² = 576 + 100
• ac² = 676
• ac = √676
• ac = 26

Hence,

• Radius of the circle = 26cm

Additional :-

let's find area of the circle :-

• a = πr²
• a = 22/7 x 26 x 26
• a = 14872/7
• a = 2124.57cm²

Hope it helps