Given unit circle P. Points A and B are on the circle (r=1), forming an acute angle APB (theta). What line segment is equal to the tangent theta if line segment DC is tanget to circle at point b.
Hello, Pat722!
The directions are somewhat fuzzy.
I may have misinterpreted them.
$\displaystyle \text{Given unit circle }P\text{, points }A,B\text{ are on the circle, forming}$
$\displaystyle \text{acute angle }AP\!B \,=\,\theta.\;\text{What line segment is equal to }\tan\theta$
$\displaystyle \text{if line segment }DC\text{ is tangent to circle at point }B\,?$
I believe the diagram looks like this:
We have the unit circle with center $\displaystyle P$ and radii $\displaystyle P\!A = PB = 1.$Code:E o .: . : . : * * * A. : * o o D * / * | * 1 / *| / | * / @ * * o - - - - o B * P 1 * | * *| * * | * * o * * * C
$\displaystyle \theta \,=\,\angle AP\!B,\;\theta \,<\,90^o$
$\displaystyle CD$ is tangent to the circle at $\displaystyle B.$
Extend $\displaystyle CD$ to meet $\displaystyle P\!A$ extended at $\displaystyle E.$
Then: .$\displaystyle \tan\theta \,=\,\frac{EB}{1}$
Therefore: .$\displaystyle EB \:=\:\tan\theta$