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: .