Question

Two chords AB, CD of lengths 5 cm, 11 cm respectively of a circle are parallel, If the distance between AB and CD is 3 cm, find the radius of the circle.

Answer 1

Let AB and CD be two parallel chord of the circle with centre O such that AB = 5 cm and CD = 11 cm. let the radius of the circle be cm.

Draw and as well as point O, Q and P are collinear.

Clearly, PQ = 3 cm

Let then

In we have

…… (1)

And

…… (2)

From (1) and (2) we get

$$\begin{gathered} \Rightarrow 6x+\frac{61}{4}=\frac{121}{4} \\ \Rightarrow 6x=\frac{121-61}{4} \\ \Rightarrow 6x=\frac{60}{4} \\ \Rightarrow x=\frac{5}{2} \end{gathered}$$

Putting the value of x in (2) we get,