Question

In the given figure, AOB is a diameter of a circle with centre O such that AB = 34 cm and CD is a chord of length 30 cm. Then, the distance of CD from AB is

(a) 8 cm

(b) 15 cm

(c) 18 cm

(d) 6 cm

Answer 1

(a) 8 cm

Join OC. Then OC = radius = 17 cm
$CL=\frac{1}{2}CD=\frac{1}{2}\ast 30cm=15cm$CL=1/2C
In right ΔOLC, we have:
$O{L}^2=O{C}^2-C{L}^2$
= $(17{)}^2-(15{)}^2$
= (289 - 225) = 64
⇒OL=√64= 8 cm
∴ Distance of CD from AB = 8 cm