Question

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

Answer 1

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