Question

Find the area of the given triangle $△XYZ$ in arbitrary units whose one of the sides passes through the center of the circle.

• A. $10$
• B. $20$
• C. $10{\text{unit}}^2$
• D. $20{\text{unit}}^2$

Answer 1

The correct option is C $10{\text{unit}}^2$

$△XYZ$ is a right triangle as the angle subtended by the diameter ZY to X on the circle is equal to ${90}^o.$

Hence, $\angle X={90}^o.$
$\therefore$ Side $XY$ is perpendicular to the side $XZ.$
$\Rightarrow XY$ can be considered as the height, and $XZ$ as the base of the triangle.

We know that area of triangle
$=\frac{1}{2}\times \text{base}\times \text{height}$

$\therefore$ Area $=\frac{1}{2}\times 4\text{units}\times 5\text{units}=10{\text{units}}^2$