Question

(2 Marks)
4. AB and CD are two parallel chords of a circle which are on opposite sides of the centre such that AB = 24 cm and CD = 10 cm and the distance between AB and CD is 17 cm. Find the radius of the circle.​

Answer 1

Given:-

AB = 24cm

CD = 10cm

distance between AB and CD is 17 cm.

To Find:-

the radius of the circle.

Understanding concept:-

Draw a diagram,the line from the centre O meet AB at E and CD at F.

Let OF be x then OE = 17-x.

Join AO and OC.

step-by-step solution:-

In ∆ AOE,

Radius r²= 5² + (17-x)² and,-------(1)

In ∆ COF,

Radius r²= 12² + x² then ----------(2)

From equation (1) and (2)

12² + x²= 5² + (17-x)²

144 + x² = 25 + 289 -34x + x²

34x + x² - x² = 314 - 144

34x = 170

x = 5

So, r² = 12² + 5²

r² = 144 + 25

r² = 169

r = 13cm

Answer 2

r = radius of circle

x = distance of one chords from center i.e (17 - x)

r² = x² + (5)²

r² = (17−x)² + (12)²

So , x² + (5)² = (17−x)² + (12)²

x² + 25 = (17−x)² + 144

⇒x = 12

∴ r² = 144+25 = 169

⇒r = 13cm

HOPE this helps you ☺️