Question

In the given figure, O is the centre of a circle such that diameter AB = 17 cm and AC = 15 cm. BC is joined. Find the area of the unshaded part. $(Take\pi =3.14$

• A. $166.86c{m}^2$
• B. $787.92c{m}^2$
• C. $823.96c{m}^2$
• D. $847.92c{m}^2$

Answer 1

The correct option is A $166.86c{m}^2$

Given, AB is a diameter of length 17 cm and AC = 15 cm .
Then, by pythagoras theorem,
$B{C}^2=A{B}^2-A{C}^2$
$B{C}^2={17}^2-{15}^2$
$BC=8cm$

Now,
Area of unshaded part = Area of circle - Area of Δ ABC
$=\pi (r{)}^2-\frac{1}{2}\times BC\times AC$
$=3.14\times (\frac{17}{2}{)}^2-\frac{1}{2}\times 8\times 15$
$=166.86c{m}^2$
So, area of unshaded part is $166.86c{m}^2$