SOLUTION: I need an equation for finding the coordinates of the midpoint of an arc if only given the endpoint and centerpoint coordinates: A(x1,y1), B(x2,y2), CC(x,y). The arc is in a 2D Ca

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Question 55098: I need an equation for finding the coordinates of the midpoint of an arc if only given the endpoint and centerpoint coordinates: A(x1,y1), B(x2,y2), CC(x,y). The arc is in a 2D Cartisian plane in Quadrant I but can be in any orientation. I already tried some solutions using the chord of AB and the cosine of the arcangle, but these only worked in certain orientations.
Any help is greatly appreciated!
Answer by Hook(36) (Show Source):
You can put this solution on YOUR website!
I think you're on the right track. I'm going to get away from the trig part, though.
Here's the tack I think you should take.
1) Find the midpoint of chord AB. I'll call that point M.
2) Prove that the line from C through M must also go through the midpoint of your arc(if its a geometry class. It may be acceptable to just throw that statement on the table in an Algebra class).
3) Find the equation of the line that passes through M and C
4) figure out where the line intersects your arc.
Let me know if that's enough direction for ya...