Here's a nice use of circle theorems: ever wondered why the sine rule works?

Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008.
He lives with an espresso pot and nothing to prove.

Colin, I always tried to teach this as “in any triangle, the ratio of a side to the sine of the opposite angle is twice the radius, and wrote “corrections” to every textbook author who wrote the law of sines with “Sin A / a” instead of with sides on top….alas, I have mellowed now.
btw, your students may be interested in knowing that it seems the term “Law of sines” was first applied to the spherical law, then extended to the planar version.

## Pat Ballew

Colin, I always tried to teach this as “in any triangle, the ratio of a side to the sine of the opposite angle is twice the radius, and wrote “corrections” to every textbook author who wrote the law of sines with “Sin A / a” instead of with sides on top….alas, I have mellowed now.

btw, your students may be interested in knowing that it seems the term “Law of sines” was first applied to the spherical law, then extended to the planar version.

## Colin

Oh, I didn’t know about the spherical version! That’s neat ðŸ™‚

## Graciela Rhodes

I like this proof. I have not thought of it before. Thank you.