Thread: circle, tangent

Line segment BA is tangent to the circle at A. CF is tangent to the circle at F. Express the length of DE in terms of θ.

Thanks so much.

I know it is 4(some identity)θ???

Hello, daydreembelievr!

Line segment is tangent to the circle at
is tangent to the circle at
Express the length of in terms of

In right triangle O\cdot\sin\theta" alt="DEO\!:\;\;\sin\theta \:=\:\frac{DE}{DO} \quad\Rightarrow\quad DE \:=\O\cdot\sin\theta" />

But is a radius of the circle: .

Therefore: .