Question

A circle is radius 5cm find the length of the chord of distance 3cm from its centre.​

Answer 1

☆ Answer ☆

8cm .

☆ Explanation ☆

Step 1 : Frist we will write the Given radius of the Circle

AC = 5cm .

AO = 3cm .

Step 2 : Consider that AOC is the right angled triangle.

Step 3 : Apply Pythagoras Theorem

AO² + OC² = AC²

3² + OC² = 5²

9 + OC² = 25

OC² = 16

Step 4 : Take square root

O C = 4

Length of Chord = 4+4=8cm .

Answer 2

$\underline\mathfrak{Given:-}$

• Radius of the chord of distance 3cm.
• Distance of the chord from its chord = 3cm.

$\underline\mathfrak{To \: \: Find:-}$

• Find the length of the chord ......?

$\underline\mathfrak{Solutions:-}$

• Let AOB is a right angle triangle

(By using the Pythagoras Theorem)

$\: \: \: \: \: \leadsto \: \: {AO}^{2} \: + \: {OB}^{2} \: \: = \: \: {AB}^{2}$

$\: \: \: \: \: \leadsto \: \: {(3)}^{2} \: + \: {OB}^{2} \: \: = \: \: {(5)}^{2}$

$\: \: \: \: \: \leadsto \: \: {9} \: + \: {OB}^{2} \: \: = \: \: {25}$

$\: \: \: \: \: \leadsto \: \: {OC}^{2} \: \: = \: \: {25} \: - \: {9}$

$\: \: \: \: \: \leadsto \: \: {OC}^{2} \: \: = \: \: {16}$

$\: \: \: \: \: \leadsto \: \: {OC} \: \: = \: \: {\sqrt{16}}$

$\: \: \: \: \: \leadsto \: \: {OC} \: \: = \: \: {4}$

Length of the chord = 4 + 4 = 8cm.

Hence, the length of the chord is 8 cm.

1. Diameter of a circle = 2 × r
2. Circumference of a circle = 2πr
3. Area of a circle = πr²

where,

• π = 22/7
• r = radius
• d = diameter