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

$\mathrm{CL}=\frac{1}{2}\mathrm{CD}=\left(\frac{1}{2}\times 30\right)\mathrm{cm}=15\mathrm{cm}$
In right ΔOLC, we have:
OL² = OC² - CL² = (17)² - (15)² = (289 - 225) = 64
$\Rightarrow \mathrm{OL}=\sqrt{64}=8\mathrm{cm}$
∴ Distance of CD from AB = 8 cm