Questions tagged [euclidean-geometry]

Geometry assuming the parallel postulate: in a plane, given a line and a point not on that line, there is exactly one line parallel to the given line through the given point.

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+50

Constructing the center of a circle, straightedge only. Variants on the Poncelet-Steiner Theorem

The Wikipedia Poncelet-Steiner Theorem entry says: Any Euclidean construction possible with straightedge and compass can be done with straightedge alone, provided that at least one circle with its ...
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+100

Prove $EK'||BX\Leftrightarrow EK'=2EK$ in a given triangle $EBC$ with $\angle E=90^\circ\;\ldots$

In a given triangle $EBC$ $\ \angle E=90^\circ$, $D\in BC$ such as $ED\perp BC$, $M'$ is midpoint of $BE$, line $CM'$ intersects the circumcircle of $\triangle EBC$ second time in $X$. $A$ is the ...