Question

O is the centre of the circle. OM ⊥ chord AB and ON ⊥ chord CD. AB = 40 cm, OM = 15 cm, ON = 7 cm.

Find the

1. radius of the circle,
2. length of the chord CD.

Answer 1

Step 1: 

`AM = (AB)/2`

AM = `40/2` = 20 cm

Step 2:

In right triangle OMA,

OA² = OM² + AM²

OA² = 15² + 20²

OA² = 225 + 400 = 625

OA = `sqrt(625)` = 25 cm

The radius r = OA = 25 cm.

Step 3:

In right triangle ONC,

OC² = ON² + NC²

Since OC is the radius, OC = 25 cm

25² = 7² + NC²

625 = 49 + NC²

NC² = 625 – 49 = 576

NC = `sqrt(576)` = 24 cm.

Step 4:

CD = 2 × NC

CD = 2 × 24 = 48 cm.

The radius of the circle is 25 cm and the length of chord CD is 48 cm.