A chord of a circle subtends an angle of theta radians at the centre of the circle. The area of the minor segment cut off by the chord is 1/8 of the area of the circle.

Prove that 4theta= pi + 4 sin theta

Ahhh i have no idea how to do it?

2. Hello juliak
Originally Posted by juliak
A chord of a circle subtends an angle of theta radians at the centre of the circle. The area of the minor segment cut off by the chord is 1/8 of the area of the circle.

Prove that 4theta= pi + 4 sin theta

Ahhh i have no idea how to do it?
If the radius of the circle is $\displaystyle r$, the area of the sector that makes an angle $\displaystyle \theta$ at the centre is $\displaystyle \tfrac12r^2\theta$. The area of the triangle with two sides of length $\displaystyle r$ enclosing an angle of $\displaystyle \theta$ is $\displaystyle \tfrac12r^2\sin\theta$.

So the area of the segment $\displaystyle = ... - ... = \tfrac18\pi r^2$

Fill in the gaps; multiply both sides by $\displaystyle 8$, divide by $\displaystyle r$ and you're there.

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### a chord of a circle subtends an angle of theta

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