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The most-used straightedge-and-compass constructions include: Constructing the perpendicular bisector from a segment; Finding the midpoint of a segment. Drawing a perpendicular line from a point to a line. Bisecting an angle; Mirroring a point in a line; Constructing a line through a point tangent to a circle; Constructing a circle through 3 ...
Draw lines AM and CM (both in light green), connecting the segment midpoint with each of the circle centers. Construct a line j (in purple) passing through point B, and perpendicular to AM. Line j is the radical axis between circle M(B) and circle A(B). Construct a line k (in dark green) passing through point D, and perpendicular to CM.
In hyperbolic geometry, one can use the standard ruler and compass that is often used in Euclidean plane geometry. However, there are a variety of compasses and rulers developed for hyperbolic constructions. A hypercompass can be used to construct a hypercycle given the central line and radius. [ 3 ] A horocompass can be used to construct a ...
Compass equivalence theorem. In geometry, the compass equivalence theorem is an important statement in compass and straightedge constructions. The tool advocated by Plato in these constructions is a divider or collapsing compass, that is, a compass that "collapses" whenever it is lifted from a page, so that it may not be directly used to ...
Mohr–Mascheroni theorem. In mathematics, the Mohr–Mascheroni theorem states that any geometric construction that can be performed by a compass and straightedge can be performed by a compass alone. It must be understood that "any geometric construction" refers to figures that contain no straight lines, as it is clearly impossible to draw a ...
To make the perpendicular to the line AB through the point P using compass-and-straightedge construction, proceed as follows (see figure left): Step 1 (red): construct a circle with center at P to create points A' and B' on the line AB, which are equidistant from P.
This line can be drawn either by using again the right triangular ruler, or by using a traditional straightedge and compass construction. With a similar construction, one can improve the location of E, by using that it is the intersection of the line SE and its perpendicular passing through A.
Radical axis. In Euclidean geometry, the radical axis of two non-concentric circles is the set of points whose power with respect to the circles are equal. For this reason the radical axis is also called the power line or power bisector of the two circles. In detail: For two circles c1, c2 with centers M1, M2 and radii r1, r2 the powers of a ...