# Math Help - circle, tangent

1. ## 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???

2. Hello, daydreembelievr!

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 $\theta.$

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

But $DO$ is a radius of the circle: . $DO \:=\:4$

Therefore: . $DE \;=\;4\sin\theta$