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Math Help - minimum distance point_1-circle-point_2

  1. #1
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    Wink minimum distance point_1-circle-point_2

    Can anibody help me to find point_C on circle where the distance { point_1-point_C-point_2 } is the shortest . Point_1 and point_2 are outside of circle.

    ( In othe words , point_C should be the image of point_1 on circle from the point_2 view , and oposite point_C should be the image of point_2 on circle from the point_1 view )

    Thanks

    thanks
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  2. #2
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    Quote Originally Posted by medison View Post
    Can anibody help me to find point_C on circle where the distance { point_1-point_C-point_2 } is the shortest . Point_1 and point_2 are outside of circle.

    ( In othe words , point_C should be the image of point_1 on circle from the point_2 view , and oposite point_C should be the image of point_2 on circle from the point_1 view )

    Thanks

    thanks
    1. Choose an arbitrary point A on the circle line.

    2. Connect P_1 with A and P_2 with A.

    3. Draw a circle around M with r = \overline{MP_2}. This circle intersects AP_1 in P_2'

    4. Construct the perpendicular bisector of \overline{P_1P_1'}

    5. This perpendicular bisector intersects the circle in C.
    Attached Thumbnails Attached Thumbnails minimum  distance point_1-circle-point_2-krspkt_minentfrng.png  
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