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Find perpendicular intersection bet. pt & circle

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Old   July 26, 2007, 05:08
Default Find perpendicular intersection bet. pt & circle
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zonexo
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Hi,

Suppose I've a circle and there's a pt A inside the circle. The pt is not at the center of the circle. If I want to find a point C on the circle such that the AC is perpendicular to the circle, what is the best way to do it?

Will there be more than 1 possible values? I'm actually looking for the pt C where AC is the shortest possible.

I have the circle's radius, its center coordinates and pt A's coordinate. I would like to obtain C's coordinate.

Thank you for your help.
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Old   July 26, 2007, 08:06
Default Re: Find perpendicular intersection bet. pt & circ
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ag
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Maybe I'm just thinking slow this morning, but wouldn't AC simply be the continuation of the segment OA from the center of the circle along the radius directed along OA? If so then C is simply the intersection of the radius that A lies on with the circle. This also implies that there is only one solution.
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Old   July 26, 2007, 20:07
Default Re: Find perpendicular intersection bet. pt & circ
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zonexo
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ops ... in that case, I'm thinking even slower ... guess I'm thinking too complicated. but so there should be 2 solutions, since the line OA can extend in 2 directions.
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Old   July 27, 2007, 08:53
Default Re: Find perpendicular intersection bet. pt & circ
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ag
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Well the line can extend in both directions, but you asked for the closest intersection point. Unless you're at the center, you'll have one answer.
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