Question

Find the length of the third side and the area of a triangle inscribed in a circle of radius 4 cm with one of its side equal to the length of diameter, another side, as well as height equal to the radius of the circle.

• A. $4\sqrt{3}cm$, $16c{m}^2$
• B. $4\sqrt{2}cm$, $16\sqrt{2}c{m}^2$
• C. $8\sqrt{2}cm$, $16\sqrt{2}c{m}^2$
• D. $9\sqrt{3}cm$, $16\sqrt{3}c{m}^2$

Answer 1

The correct option is A

$4\sqrt{3}cm$, $16c{m}^2$

Triangle formed by taking diameter is always a right-angled at the circumference.

3rd side of triangle = $\sqrt{8^2-4^2}$

= $4\sqrt{3}cm$

Area= $\frac{1}{2}\times 8\times 4$

= $16c{m}^2$