Question

In the given figure, CD is the diameter of a circle with centre O and CD is perpendicular to chord AB. If AB = 12 cm and CE = 3 cm, then radius of the circles is
(a) 6 cm
(b) 9 cm
(c) 7.5 cm
(d) 8 cm

Answer 1

(c) 7.5 cm
Let OA = OC = r cm.
Then OE = (r - 3) cm and $\mathrm{AE}=\frac{1}{2}\mathrm{AB}=6\mathrm{cm}$
Now, in right ΔOAE, we have:
OA² = OE² +AE²
⇒ (r)² = (r - 3)² + 6²
⇒ r² = r² + 9 - 6r + 36
⇒ 6r = 45
⇒ $r=\frac{45}{6}=7.5$ cm
Hence, the required radius of the circle is 7.5 cm.