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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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