Question

Circle with centre O and radius $25cms$ has a chord AB of length of $14cms$ in it. Find the area of triangle AOB?

Answer 1

REF.Image.

r = 25 cm

AB = 14 cm.

$ar△AOB=?$

$\because OA=OB$

So, $△AOB$ os an isosceles triangle.

$\Rightarrow$ Area of $△AOB=\frac{r}{4}\times [4r^2-(AB{)}^2{]}^1/2$

$[\because$ Area of isosceles $△$ is given by $\frac{h}{4}\times [4a^2-b^2{]}^{1/2}$ where 'a' is side and 'b' is the base of $△$ ]

$\Rightarrow \frac{r}{4}\times [4r^2-(AB{)}^2{]}^{1/2}$

$=\frac{25}{4}[4\times 625-(14{)}^2{]}^{1/2}$

$Ar\left(△AOB\right)\Rightarrow 168c{m}^2$