Question

Let A = (0,12) and B = (25,12). If possible, find coordinates for a point P on the x-axis that makes angle APB a right angle.

Answer 1

@skullpatrol @zepdrix

Answer 2

Hint:
The diameter of a circle subtends a right angle at the circumference.

Answer 3

As usual, geometry problems are half solved if you start drawing a diagram of the given information.

Answer 4

What do you mean when you say that the "diameter of a circle subtends aright angle at the circumference"? @mathmate

Answer 5

sorry consider D as P

Answer 6

But how will APB become a right angle?

Answer 7

@calculusxy

If AB is a diameter of a circle, then any point C, C'... on the circumference makes a right angle, i.e. ACB=AC'B=AC''B...=90 degrees.
Use this hint to solve your problem.

Answer 8

So I understand that now but the thing that I'm currently stuck on is solving for the C on the x-axis. I know that having a circle works but it's just the thing with drawing it and solving to find the coordinate.

Answer 9

Use metric relations to solve for x.
(x)(25-x)=12^2