Question

What is the area of a right angled triangle if the radius of its circumcircle is 3 cm and altitude drawn to the hypotenuse is 2 cm?

• A. $6c{m}^2$
• B. $4c{m}^2$
• C. $5c{m}^2$
• D. $3c{m}^2$

Answer 1

The correct option is A $6c{m}^2$

In the case of a right triangle, the hypotenuse is a diameter of the circumcircle, and its center is exactly at the midpoint of the hypotenuse.

As radius of its circumcircle is 3 cm, so AC (hypotenuse) = $3\times 2=6cm$.
$BD=2cm$

Area of triangle ABC = $\frac{1}{2}\times AC\times BD$

Area = $\frac{1}{2}\times 6\times 2$

Area = $6c{m}^2$