Question

Find the area of the minor segment of a circle if the area of the circle is $100c{m}^2$ and the area of the major segment is $70c{m}^2$.

• A. $170c{m}^2$
• B. $130c{m}^2$
• C. $30c{m}^2$
• D. $200c{m}^2$

Answer 1

The correct option is C $30c{m}^2$

We know that major and minor segment combined together form the circle.
From the figure,
ACB is minor segment and ADB is major segment.
Area of ACB + Area of ADB = Area of the circle.
Hence, Area of ACB + 70 = 100
$\Rightarrow$ Area of ACB = 100 - 70 = 30 $c{m}^2$
Thus, the area of the minor segment is $30c{m}^2$