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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

  • Math -

    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 -

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

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