Question

a chord of length 24cm is at a distance of 5cm form the center of the circle . the length of the chord of the same circle which is at a distance of 12cm form the center is . answer please​

Answer 1

Question

A chord of a length 24 cm is at distance of 5 cm from the centre of the circle. Find the length of the chord of the same circle which is at a distance of 12 cm from the centre.

Given

• Length of chord is 24 cm which is at distance of 5 cm from the centre of the circle.

Required to Find

Length of the chord of the same circle which is at a distance of 12 cm from the centre.

Solution

Let AB be the chord of length 24 cm and O be the centre of the circle.

Let OC be the the perpendicular to a chord , from the centre of a circle , bisect the chord.

So , AC = CB = 12 cm

In ∆ OCA ,

OA² = OC² + AC²

( By Pythagoras theorem )

( 5 )² + ( 12 )² = 169

OA = 13 cm

therefore, Let A'B' be new chord at a distance of 12 cm from the centre.

( O'A')² = ( O'C' )² + ( A'C' )²

(A'C' )² = ( 13 )² - ( 12 )² = 25

A'C' = 5 cm

Hence, the length of the new chord

2 × 5 = 10 cm.