Posted by **Kole** on Tuesday, October 2, 2012 at 2:12am.

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.

- Math -
**Steve**, Tuesday, October 2, 2012 at 10:39am
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.

- Math -
**Gsidthekid**, Thursday, October 4, 2012 at 12:09am
Steve your a boss for asking this question, you just saved me 2 hours of my life trying to figure it out, YEEEE

- Math -
**Gsidthekid**, Thursday, October 4, 2012 at 12:10am
Kole*

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