Question

In the given figure PQ is the diameter of a circle with centre O, and is perpendicular to the chord AB. If AB = 8cm and QM = 2cm, find the radius of the circle.

• A. 5 cm
• B. 6 cm
• C. 2 cm
• D. 4 cm

Answer 1

The correct option is A

5 cm

OM is perpendicular to AB [perpendicular from the centre of the circle bisects the chord.]

$\therefore AM=MB=4cm$

Let radius of the circle OA be r cm.

OM = OQ - MQ $\Rightarrow$ ( r - 2) cm

Using Pythagoras theorem in right angled triangle OAM

$O{A}^2=M{A}^2+O{M}^2$

$r^2=4^2+(r-2{)}^2$

$r^2=16+r^2-4r+4$

$\Rightarrow r=5cm$