Question

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is ______.

Options

• r² sq.units

• `1/2` r² sq.units

•  2 r² sq.units

• `sqrt(2)` r² sq.units

Answer 1

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is r² sq.units.

Explanation:

The largest triangle that can be inscribed in a semi-circle of radius r units is the triangle having its base as the diameter of the semi-circle and the two other sides are taken by considering a point C on the circumference of the semi-circle and joining it by the endpoints of diameter A and B.

∴ ∠ C = 90°  .....(By the properties of circle)

So, ΔABC is right-angled triangle with base as diameter AB of the circle and height be CD.

Height of the triangle = r

∴ Area of largest ΔABC = `1/2`× Base × Height

= `1/2` × AB × CD

= `1/2` × 2r × r

= r² sq.units