Question

In the figure, given below, AB and CD are two parallel chords and O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of lengths 24 cm and 18 cm respectively.

Answer 1

Given,  AB = 24 cm, CD = 18 cm

⇒ AM = 12 cm, CN = 9 cm

Also, OA = OC = 15 cm

Let MO = y cm and ON = x cm

In right angled ∆AMO

(OA)² = (AM)² + (OM)²

⇒ 15² = 12² + y²

⇒ y² = 15² – 12²

⇒ y² = 225 – 144

⇒ y² = 81

⇒ y = 9 cm

In right angled ΔCON

(OC)² = (ON)² + (CN)²

⇒ 15² = x² + 9²

⇒ x² = 15² – 9²

⇒ x² = 225 – 81

⇒ x² = 144

⇒ y = 12 cm

Now, MN = MO + ON

= y + x

= 9 cm + 12 cm

= 21 cm