Question

Chords AB & CD of a circle are parallel to each other and lie on opposite sides of the centre of the circle. If AB = 36 cm, CD = 48 cm and the distance between the chords is 42 cm. Find the radius of the circle.

• A. 40 cm
• B. 30 cm
• C. 50 cm
• D. 18 cm

Answer 1

The correct option is B

30 cm

In $\Delta$EOB, $r^2$ = $(42-x{)}^2$+ $(18{)}^2$ ------ (i)

In $\Delta$FOD, $r^2$ = $(24{)}^2$ +$x^2$ ------ (ii)

Subtract (i) from (ii), we get

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

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

(42- 2x)(42) = 6$\times$(42)

x = 18 cm

Putting the value of x in equation (ii), we get

$r^2=(18{)}^2+(24{)}^2$

r = 30 cm