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In spherical geometry we look at the globe as the sphere S^2. Any plane intersecting the sphere will create a great circle. Now if you take any point on the globe and reflect it across that plane, you have another point that is equidistant from the plane. The sets of all these points will be equidistant from the great circle.
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How do you find a point equidistant from three other points?
To find a point equidistant from three other points, construct perpendicular bisectors for two of the segments formed from three points. Note: this will be the center of the circle that has all three points on it's circumference. Three points, not in a straight line, form three pairs of points with each pair defining a different line. Take any pair of points and draw the perpendicular bisector of the line joining them. Repeat for one of the other pairs. These two perpendicular bisectors will meet at the point which is equidistant from all three points - the circumcenter of the triangle formed by the three points.
Set of all points equidistant from a given point?
Circle!
What is an equation of the locus of points equidistant from the points 4 1 and 10 1?
Every point equidistant from (4, 1) and (10, 1) lies on the line [ x = 7 ],and that's the equation.
All the points equidistant to a given point would form?
A circle.
What is the point in a circle that is equidistant from all points on the circle?
It is the centre of the circle
