Question

If a chord $AB$ of length $8cm$ is making ${90}^o$ at the centre ${}^{\prime }{O}^{\prime }$ of a circle, the find the area of $△AOB$ (in $c{m}^2$)

• A. $10$
• B. $14$
• C. $16$
• D. $18$

Answer 1

The correct option is C $16$

In $\Delta OAB$

${\left(OA\right)}^2+{\left(OB\right)}^2={\left(AB\right)}^2$ (By pythagorus theorem)

$\Rightarrow r^2+r^2={\left(8\right)}^2$

$\Rightarrow 2r^2=64$

$\Rightarrow r^2=32$

Area of $\Delta OAB$$=\frac{1}{2}\times OA\times OB$

$=\frac{1}{2}\times r\times r$

$=\frac{1}{2}\times 32$

$=16$ $c{m}^2$