I have the following problem. In the figure, the circumference is tangent to the Y-axis in the point P, the point A has coordinates (2,0) and OA=AB. I am asked to calculate the coordinates of the point P.
This is what I thought: I want to calculate the center of the circumference, given that I know the coordinates of two points in it. If I call this center C, then, for example, AC=PC, and knowing what the distance between two points is, I'd be able to find the coordinates of the point P. However, I am not being able to find the coordinates of the center.
I am supposed to be able to solve this with a not so advanced math. Any ideas?
The center of the circle is $(3, b)$. $3$ came from mid point between A and B, and it's also the radius of the circle. And $$b^2=r^2-1^2=3^2-1=8$$ So $P=(0,2\sqrt2)$.