Question

The radius of a circle with center O is $5$ cm. two radii OA and OB are drawn at right angles to each other. Find the area of segments made by chord AB.

Answer 1

$AB=\sqrt{25+25}=\sqrt{50}=5\sqrt{2}cm$

Major area of $AB=$ Area of shaded part $+ar\left(\Delta AOB\right)$

$=\frac{3}{4}\pi r^2+\frac{1}{2}+b\times h$

$=(\frac{3}{4}\times 3.14\times 5\times 5)+\frac{1}{2}\times 5\times 5$

$=58.87+12.5$

$=71.37c{m}^2$

Minor area of $AB=\frac{1}{4}$ quadrant of circle $-ar\left(\Delta AOB\right)$

$=\frac{1}{4}\times \pi r^2-\frac{1}{2}\times b\times h$

$=\frac{1}{4}\times 3.14\times 5\times 5-\frac{1}{2}\times 5\times 5$

$=19.62-12.5$

$=7.12c{m}^2$