#### 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, fins the distance MN between the two chords of lengths 24 cm and 18 cm respectively.

#### Solution

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 âˆ†AMO

`(OA)^2 = (AM)^2 + (OM)^2`

⇒ `15^2 = 12^2 + y^2`

⇒ `y^2 = 15^2 -12^2`

⇒ `y^2 = 225 -144`

⇒` y^2 = 81`

⇒ y = 9 cm

In right angled ΔCON

`(OC)^2 = (ON)^2 + (CN)^2`

⇒ `15^2 = x^2 + 9^2`

⇒ `x^2 =15^2 - 9^2`

⇒` x^2 = 225 - 81`

⇒ `x^2 = 144`

⇒ y = 12 cm

Now, MN = MO + ON

= y + x

= 9 cm +12 cm

= 21 cm

Is there an error in this question or solution?

Solution 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, Fins the Distance Mn Between the Two Chords of Lengths 24 Cm and 18 Cm Respecti Concept: Arc and Chord Properties - Angle in a Semi-circle is a Right Angle.