Question

Find the area of the right triangle PQY, right-angled at Q, having P as the center of the circle of radius 5 units. The length of the chord ZY is 8 units.
square units

Answer 1

P is the centre of the circle.

$PY=5\text{units}$ (radius)

$△PQY$ is a right triangle with $\angle Q={90}^o.$
$\therefore PQ$ is the line perpendicular to the chord $ZY$ from the center of the circle.

Hence, $QY=\frac{ZY}{2}=\frac{8}{2}=4\text{units}.$

PY is the hypotenuse the given triangle.
$\therefore P{Q}^2+Q{Y}^2=P{Y}^2$
$\Rightarrow PQ=\sqrt{P{Y}^2-Q{Y}^2}$
$\Rightarrow PQ=\sqrt{5^2-4^2}=3\text{units}$

Area of the triangle
$=\frac{1}{2}\times \text{base}\times \text{height}$
$=\frac{1}{2}\times 4\text{units}\times 3\text{units}$
$=6{\text{unit}}^2$