Question

in a circle of radius 13 cm is drawn at a distance of 12 CM of the centre find the length of the chord

Answer 1

What is the distance from the centre to the chord in the question?

(Answer is in the comments)

Answer 2

Length of chord is 10 cm.

Given:

• In a circle of radius 13 cm.
• A chord is drawn at a distance of 12 cm from the centre.

To find:

• Find the length of the chord.

Solution:

Formula/Concept to be used:

• Perpendicular from centre of circle bisects chord.
• Apply Pythagoras theorem.
• Pythagoras theorem: It states that in right triangle Hypotenuse²= Perpendicular²+Base²

Step 1:

Draw the figure as shown on attached image.

A is centre of circle.

AB; radius= 13 cm

AD; perpendicular distance from centre= 12 cm

Step 2:

It is clear that ∆ADB is right triangle, right angle at D.

So,

Hypotenuse(AB)

Base(BD)

Perpendicular (AD)

Apply Pythagoras theorem:

AB²= AD²+BD²

$169 = 144 + BD^{2}$

or

$BD^{2} = 169 - 144$

or

$BD^{2} = 25$

or

$\bf BD = 5\:cm$

Step 3:

Find the length of chord.

As,

BC= 2 BD

So,

BC =10 cm

Thus,

Length of chord is 10 cm.

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