question_answer

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

A) \[{{r}^{2}}\]sq units

B) \[\frac{1}{2}{{r}^{2}}\]sq units

C) \[2{{r}^{2}}\]sq units

D) \[\sqrt{2}{{r}^{2}}\]sq units

Correct Answer: A

Solution :

Take a point C on the circumference of the semi-circle and join it by the end points of diameter A and B. \[\therefore \,\,\,\,\angle C=90{}^\circ \]             [by property of circle] [angle in a semi-circle are right angle] So, \[\Delta ABC\]is right angled triangle. \[\therefore \] Area of largest \[\Delta ABC=\frac{1}{2}\times AB\times CD\] \[=\frac{1}{2}\times 2r\times r\] \[={{r}^{2}}\]sq units