1. 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

2. Originally Posted by medison
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.