Question

Rohan draws a circle of radius 10 cm with the help of compass and scale. He also draws two chords, AB and CD in such a way that AB and CD are 6 cm and 8 cm from the centre O. Now, he has some doubts that are given below. Help him out by answering these questions:

a)what will be the chord of ab?
b)what wil be the chord of cd?​

Answer 1

Length of AB = 16 cm

h² = p² + b²

10² = 6² + b²

100 = 36 + b²

`b = √(64)`

`= 8 cm`

`AB = 8 + 8`

`= 16 cm`

Answer 2

• a) 16 cm
• b) 12 cm

Explanation:

Connect the center with A and C:

• OA = 10 cm or OC = 10 cm

Use Pythagorean to find half of AB:

• 
  `AB/2=√(10^2-6^2) =√(64) =8`
• 
  `AB = 16`

Similarly, find the length of CD:

• 
  `CD/2=√(10^2-8^2) =√(36) =6`
• 
  `CD=12`