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Question
circle
circle  
Let A and B be the endpoints of a diameter of a circle. Let C be any point of the same circle. Show that the segments CA and CB are perpendicular.

Hint: I recommend using vector v =vector AM and vector w = vector MC"

I cannot seem to get an answer to this problem

Answer
Note that the segments AM, MB and MC are equal (and equal to the radius of the circle). Let the angle ∠MBC = a and the angle ∠CMB = b. The triangle ∆CMB is isosceles so that ∠MCB = a. Thus 2a + b = 180 (sum of the angles of a triangle). Also, we have ∠AMC = b' and ∠CAM = ∠MCA = a' so that 2a' + b' = 180. A little algebra, along with b + b' = 180, shows that a + a' = 90.

Randy

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randy patton

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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