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Question
circle
circle  
I have been having difficulty proving this proof. Any help would be greatly appreciated.
You MUST use vectors operations and/or dot product to solve this question.

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

Answer
If we run a line from M to the center of AC, it will intersect AC at a point called D.

We can see that the length AM is 1/2 of the length of AB and the length of AD is 1/2 if the length of BC.  This makes the triangle ADB similar to triangle ACB.

It can also be seen that triangle ADM is the same ac triangle ACM
since angle ADM is the same as angle CDM, DM is the same as itself,
and AD is the same as DC (SAS rule).

Since AC is a line and the sum of angle ADM and angle ADC make up this,
and they are both angles of the same measurement, the measurement of each
is 180/2 - 90.  Hence, ACB is a right triangle.

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