Question

Find the length of a chord, which is at a distance of 24cm from the centre of a circle whose diameter is 50cm.

Answer 1

Radius of circle = 50/2 = 25 cm

perpendicular distance = 24 cm

Therefore, By Pythagoras theorem:

Hypotenuse² = Base² + Perpendicular ²

25² = Base² + 24²

Base² = 625 - 576

Base² = 49

Base = 7

Chord = 2 × Base

Chord = 2 × 7

Answer: 14 cm

Answer 2

Given: A chord is at a distance of 24cm from the centre of a circle whose diameter is 50cm.

To find: The length of a chord.

Solution:

Let the length of the chord be AB and let the centre of the circle be O. If a perpendicular is dropped from O to AB at a point C. Now, the points O, B and C form a right-angled triangle OBC. The line OC forms the perpendicular which is 24 cm, CB forms the base and OB forms the hypotenuse which is the radius of the circle.

The diameter of the circle is 50 cm so the radius of the circle would be 25 cm. Now, the length of CB can be found using the Pythagoras theorem.

$CB = \sqrt{(25)^{2} - (24)^{2}}$

      $= 7 cm$

Now the length of the entire chord can be calculated as follows.

$AB = AC + CB$

      $= 2CB$

      $= 14 cm$

Therefore, the length of a chord is 14 cm.