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 $\displaystyle BA$ is tangent to the circle at $\displaystyle A.$
$\displaystyle CF$ is tangent to the circle at $\displaystyle F.$
Express the length of $\displaystyle DE$ in terms of $\displaystyle \theta.$
In right triangle $\displaystyle DEO\!:\;\;\sin\theta \:=\:\frac{DE}{DO} \quad\Rightarrow\quad DE \:=\O\cdot\sin\theta$
But $\displaystyle DO$ is a radius of the circle: .$\displaystyle DO \:=\:4$
Therefore: .$\displaystyle DE \;=\;4\sin\theta$