Question

Let A, C be the endpoints of the diameter of a circle and B an arbitrary point on the circle. Using the
slopes of secant lines show that \ABC is a right angle. You can assume the circle is centered at the
origin.

Answer 1

we can without loss of generality assume the radius is 1, and the diameter is on the x-axis. the coordinates of B are (cosθ,sinθ).

slope of AB = sinθ/(1+cosθ)
slope of CB = -sinθ/(1-cosθ)

product of slopes: -sin^2 θ/(1-cos^2 θ) = -1

so, the lines are perpendicular.

Answer 2

Steve your a boss for asking this question, you just saved me 2 hours of my life trying to figure it out, YEEEE

Answer 3

Kole*