# Thread: Length of a curved triangle on a circle

1. ## Length of a curved triangle on a circle

Hi there! New to the forum so, hi guys!

Sorry if this is an easy one but my mind's gone blank on this. Trying to work out the length of the red line in the attached picture, given the radius of the circle, the length of the (quasi) adjacent side and the top angle.

Thanks for any help or the equation for this! Cheers guys,

PA

2. ## Re: Length of a curved triangle on a circle

draw another radius to form a triangle and use the law of sines

3. ## Re: Length of a curved triangle on a circle

Gotcha, sorry I was having a real brain fart there, of course two triangles are possible given the variables.

one triangle

6. ## Re: Length of a curved triangle on a circle

Yes two triangles possible depending on point A or D

7. ## Re: Length of a curved triangle on a circle Originally Posted by psychoangus Yes two triangles possible depending on point A or D
Only one triangle makes sense for finding the arc length you are looking for...

8. ## Re: Length of a curved triangle on a circle Originally Posted by SlipEternal Only one triangle makes sense for finding the arc length you are looking for...
Yes of course! I'm just saying, the maths could be done to give two possible outcomes.

9. ## Re: Length of a curved triangle on a circle Originally Posted by SlipEternal Only one triangle makes sense for finding the arc length you are looking for... Originally Posted by psychoangus Yes of course! I'm just saying, the maths could be done to give two possible outcomes.
If we look at this attachment If $\overline{BA}$ were tangent to the circle then the question is trivial. But that is not given.

We do know that $\frac{1}2{}(\hat{DE}-\hat{AF})=\frac{\pi}{3}$ The are $m(\hat{FDE})=\pi$

10. ## Re: Length of a curved triangle on a circle

Yep thanks for all your help guys.