New posts in Plane Geometry

Intersection of perpendicular chords: is this true for a sphere?

First year french college. Is there a finite set of points of the plane A. Finite set of point A such as...

How to prove that the points $E, F, G$ are collinear

Six points on an ellipse: generalizing Conway's Circle Theorem

A generalization of Bottema's theorem

Suppose $\angle BAC = 60^\circ$ and $\angle ABC = 20^\circ$. A point $E$ inside $ABC$ satisfies $\angle EAB=20^\circ$ and $\angle ECB=30^\circ$.

Calculate the distance of any point on the arc from the center of circle

Given $\triangle ABC$ can we construct point $O$ such that $AO\times BC=BO\times AC=CO\times AB$?

$\triangle ABC$ with a point $D$ inside has $\angle BAD=114^\circ$, $\angle DAC=6^\circ$, $\angle ACD=12^\circ$, and $\angle DCB=18^\circ$.

Olympiad question: In the regular pentagon $ABCDE$, the perpendicular at $C$ to $CD$ meets $AB$ at $F$. Prove that $AE + AF = BE$.