Drop a Perpendicular to a Line from a Point

Geometric Construction with the Compass Alone

A segment AB is given by its end points A and B. Find a point C such that AC is perpendicular to AB.

Solution

Before attempting this problem you should look into the first one.

With an arbitrary radius R ≥ AB draw two circles with centers at A and B. Let O be one of the points of intersection. With the center O and the same radius R draw a circle and then use the first problem to find the point C opposite the point B on this circle. Then AC is perpendicular to AB.

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