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What is the area of the largest triangle...

What is the area of the largest triangle that can be inscribed in a semicircle of radius r unit.

A

`r^(2)` sq units

B

`(1)/(2)r^(2)` sq units

C

`2r^(2)` sq units

D

`sqrt(2)r^(2)` sq units

Text Solution

Verified by Experts

The correct Answer is:
A
Take a point C on the circumference of the semi-circle and join it by the end points of diameter A and B.
`:. angleC= 90^(@)` [by proyerty of circle]
[angle in a semi-circle are right angle]
So, `DeltaABC` is right angled triangle.
`:.` Area of largest `DeltaABC = (1)/(2)xxABxxCD`
= `(1)/(2)xx2rxxr`
= `r^(2)` sq units ltBRgt
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