and 
be points on a plane such that 
Let 
be a point on that plane such that 
Prove that ![$$AP \in \left[\frac{5-\sqrt{5}}{10}, \frac{-1+\sqrt{5}}{2}\right] \cup \left[\frac{5+\sqrt{5}}{10}, \frac{1+\sqrt{5}}{2}\right].$$](http://latex.artofproblemsolving.com/7/8/e/78e428cbc99ce4e9448f5c4cec86f50567123812.png)
be reals such that 
. Prove that
specifies the greatest common divisor of 
and 
.
Y by Mango247, Mango247, Mango247
The triangle 
is isosceles, with 
and 
. The point 
inside the triangle is considered such that 
and 
. Find the measure of the angle 
.
is isosceles, with 
and 
. The point 
inside the triangle is considered such that 
and 
. Find the measure of the angle 
.This post has been edited 2 times. Last edited by parmenides51, Jun 8, 2020, 8:28 AM
