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Question

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

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

##### Expertise

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

##### Experience

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

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

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

Past/Present Clients
Also an Expert in Oceanography