circle, tangent

• November 7th 2008, 08:06 PM
daydreembelievr
circle, tangent
http://i46.photobucket.com/albums/f1...schic/0000.jpg

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???
• November 7th 2008, 08:26 PM
Soroban
Hello, daydreembelievr!

Quote:

http://i46.photobucket.com/albums/f1...schic/0000.jpg

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 $DEO\!:\;\;\sin\theta \:=\:\frac{DE}{DO} \quad\Rightarrow\quad DE \:=\:DO\cdot\sin\theta$

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

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