Question

A chord of length 8 cm is drawn at a distance of 3 cm from the centre of a circle. Calculate the radius of the circle.

• A. 4 cm
• B. 5 cm
• C. 8 cm
• D. 9 cm

Answer 1

The correct option is B

5 cm

In the circle, O is the centre chord AB = 8 cm.

OM $\perp$ AB which bisects it at M.

$\therefore AM=\frac{1}{2}AB=\frac{1}{2}\times 8=4\text{cm}$

OM = 3 cm

Now in right $\Delta OAM$,

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

$=(4{)}^2+(3{)}^2=16+9=25$

$\therefore OA=\sqrt{25}=5\text{cm}$