Hello, TheJacksonater!
Prove: .if , then: . Let: .
Then: .
. And: .
Since , we have: .
. .
. .
Therefore: .
Prove that the angle formed by joining any point
on a circle to the endpoints of a diameter is 90°. Let the circle be: .
Let be the endpoints of the diameter.
Let be any point on the circle.
Draw segments and Code:

* * *
*  * C
*  o(r·cosθ,r·sinθ)
*  / *
 /
*  / θ *
 B o     *     o A  
(r,0)*  *(r,0)

*  *
*  *
*  *
* * *

Then: .
. . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
Therefore: .