# Find the area of the minor segment.

Find the area of a minor segment formed by a circle of radius $6 cm$ and a chord whose distance from the centre of the circle is $3cm$.

I tried it in this way:

So i tried finding out $\theta$ which is $2.094$ $rad$, then I found the area using this: $\frac{1}{2}r^2\theta$, i get $37.7$ $cm^2$ but that is wrong.... what is my error?

## 1 Answer

The angle is $\frac{2\pi}{3}$. For draw the chord, and join its endpoints $A$ and $B$ to the centre $O$ of the circle. Drop a perpendicular from $O$ to the midpoint $M$ of $AB$.

Then $\frac{OM}{OA}=\frac{3}{6}=\frac{1}{2}$, so $\angle AOM$ is $\frac{\pi}{3}$. Double to get the angle subtended by the chord.

You had done this. But you then found the area of the sector, not the area of the segment. From the area of the sector, we need to subtract the area of a triangle with height $3$ and base $(2)(6)\frac{\sqrt{3}}{2}$.

• i did this....i hope you can see my answer....but the area doesn't come out! what is your area? – Kiara Apr 13 '14 at 21:02
• I have added to the post. You calculated the area of the circular sector correctly, but that is not what is asked for. – André Nicolas Apr 13 '14 at 21:09
• You are welcome. – André Nicolas Apr 13 '14 at 21:11