Question

If the radius of a circle is 13 cm and the length of its chord is 10 cm then what is the distance of chord from the centre?

Answer 1

Answer:

Distance of chord from center = 12 cm.

Step-by-step explanation:

Given,

Radius of a circle is 13 cm.

Length of its chord is 10 cm.

To find: the distance of chord from the centre

Solution:

Since, Length of chord is always perpendicular to the distance of chord from center.

It will result into the formation of a right angled triangle with base equal to half of the length of chord and hypotenuse = radius. and distance of chord from the center as Perpendicular of right angled triangle.

i.e. Base of right angled triangle = 10/2 = 5 cm

And hypotenuse = 13 cm

Then, Perpendicular :

$\sqrt{(13)^2 - (5)^2} \\\\=\sqrt{169 - 25} = \sqrt{144} = 12 \ cm$

Therefore, Distance of chord from center = 12 cm.

Answer 2

$\Large{\underbrace{\underline{\sf{Understanding\; the\; Question}}}}$

Here in this question, concept of properties of circle as well as Pythagoras theorem is used. We are given length of radius and chord of circle and we have to find the distance between chord and centre. We know that whenever a line segment from centre meèts chord, it divides the chord perpendicularly. To find distance of chord from centre, we will use Pythagoras theorem.

So let's start!!

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Solution:-

Distance of BD=10cm

As line segment from centre divides it perpendicularly, so:

⇒ BC=½BD

⇒ BC=½(10cm)

⇒ BC=5cm

~∆BCA is a right angled triangle.

In ∆ BCA, by applying Pythagoras theorem:

⇒ Hypotenuse ²=Base²+Perpendicular ²

⇒ (13cm)²=(5cm)²+AC²

⇒ 169cm²=25cm²+AC²

⇒ 169cm²-25cm²=AC²

⇒ 144cm²=AC²

⇒ √144cm²=AC

⇒ 12cm=AC

So the distance of chord from centre is 12cm.

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Theorem used in solution:-

Pythagoras theorem→ According to Pythagoras theorem,In a right angled triangle, the square of Hypotenuse will be equal to the sum of square of base and it's perpendicular.

★ Hypotenuse²=Base²+Perpendicular ²

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Figure attached!!