Question

Two parallel chords AB and CD are 42cm apart and lie on the opposite sides of the centre of a circle. If AB = 36cm and CD = 48cm, find the radius of the circle.

• A. 30 cm
• B. 35 cm
• C. 10 cm
• D. 20 cm

Answer 1

The correct option is A

30 cm

AB = 36 cm, CD = 48cm and PQ = 42 cm

AP = PB = $\frac{1}{2}$ AB = 18 cm

CQ = DQ = $\frac{1}{2}$ CD = 24cm

Let OQ = x cm, then OP = (42 - x) cm

Join OA and OC

OA = OC = r, radius of the circle

In right angled triangle $△$ OAP

$O{A}^2=O{P}^2+A{P}^2$

$\Rightarrow r^2=(42-x{)}^2+{18}^2$..........(i)

In right angled triangle $△$ OCQ

$O{C}^2=O{Q}^2+C{Q}^2$

$\Rightarrow r^2=x^2+{24}^2$..........(ii)

From (i) and (ii) we get

$(42-x{)}^2+{18}^2$. = $x^2+{24}^2$

$\Rightarrow 84x=1512\Rightarrow x=18$

$r^2=x^2+{24}^2$

=${18}^2+{24}^2$

= 324 + 576 = 900

r = $\sqrt{900}$ = 30 cm