Question

In the figure, the circle has a radius of $7.07$. $\overline{AC}$ is a diameter, and $AB=BC$. The area of triangle $ABC$ is

• A. $100$
• B. $200$
• C. $50$
• D. $75$
• E. $25$

Answer 1

The correct option is C $50$

As angle subtended dia on circle is ${90}^{\circ }$

$\Rightarrow \Delta ABC$ is Rt triangle $AB=BC$

$\Rightarrow A{C}^2=(2r{)}^2=(AB{)}^2+(AC{)}^2\Rightarrow AB=AC=\sqrt{2}=10$

$\therefore A=\frac{1}{2}\times AB\times AC=50$