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?
Best 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 $(2)(6)\frac{\sqrt{3}}{2}$.