Question

In the given figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to:

• A. 2 cm
• B. 3 cm
• C. 4 cm
• D. 5 cm

Answer 1

The correct option is A 2 cm

We know that, the perpendicular from the centre of a circle to a chord bisects the chord.
$AC=CB=\left(\frac{1}{2}\right)AB=\left(\frac{1}{2}\right)\times 8=4cm$
OA = 5cm (given)
$A{O}^2=A{C}^2+O{C}^2$
$\left(5^2\right)=(4{)}^2+O{C}^2$
OC = 3 cm
[Take positive value as length can't negative]
OA = OD = 5cm
CD = OD - OC = 5 - 3 = 2cm.