Question

The figure given below, shows a circle with centre O in which diameter AB bisects the chord CD perpendicularly at point E . If CD =16 cm & EB = 4 cm. find the radius of the circle.

• A. 6 cm
• B. 8 cm
• C. 10 cm
• D. 11 cm

Answer 1

The correct option is C

10 cm

Use Pythagoras Theorem

Let us assume OE = x cm
The radius of the circle will be OB = OE+EB = x+4

Using Pythagoras Theorem for $\Delta$OED we get,

${(4+x)}^2$ = ${\left(8\right)}^2$ + ${\left(x\right)}^2$

16 + $x^2$ + 8$x$ = 64 + $x^2$

$x$ = 6

Therefore Radius of circle = 4+6 = 10 cm