Is there any geometric construction for discovering a fourth point when three non-collinear points are given?
2026-05-06 05:10:42.1778044242
Given three points on a circle, finding a fourth one on the same circle
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Connect any two line segments from three dots. Make the perpendicular bisectors of both line segments. The point on which the perpendicular bisectors meet is the center of the circle with the three points we started with as points on the circumference.
Why though? Any point on the perpendicular bisector of a line segment AB is equidistant to both the end points A and B. When you take a second line segment BC, any point on the perpendicular bisector of BC is equidistant from B and C. So, the point where the perpendicular bisectors of AB and BC meet will be equidistant to A and B, and also to B and C. Thus, all the points are equidistant from the point. This happens in the circumference of a circle.
You can now mark the fourth point easily.