Question

4. Radius of a circle with centre O is 25 cm. Find the distance of a chord from the centre if length of the chord is 48 cm. *



7 cm

14 cm

8 cm​

Answer 1

Answer:

The distance of the chord from the centre is 7 cm.

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

In figure,

Point O is the centre of circle.

OA is the radius of the circle.

OB = 25 cm

AB is the chord of circle.

AB = 48 cm

We have to find the distance of the chord from the centre i. e. length of OM.

Now,

A perpendicular drawn from the centre of a circle to a chord bisects the chord.

OM ⊥ AB

∴ AM = BM = ½ * AB

⇒ BM = ½ * 48

⇒ BM = 48 ÷ 2

⇒ BM = 24 cm

Now, in △OMB, m∠M = 90°,

∴ By Pythagoras theorem,

OB² = OM² + BM²

⇒ ( 25 )² = OM² + ( 24 )²

⇒ 625 = OM² + 576

⇒ OM² = 625 - 576

⇒ OM² = 49

⇒ OM = √49

⇒ OM = √( 7 * 7 )

⇒ OM = 7 cm

∴ The distance of the chord from the centre is 7 cm.