New posts in Geometric Construction

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

Through two given points on a circle, construct two parallel chords with a given sum.

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

Construct a circle tangent to sides $BC$ and $CD$ and s.t. its meetings with the diagonal $BD$ are tangent points from tangents draw from point $A$

Prove roots of $x^5 - 1$ are constructible

How to construct an equilateral triangle on 2 concentric circles

Finding angle $x$, a geometry question

What is the next number on the constructibility sequence? And what is the asymptotic growth?

Is there a geometric construction that finds the intersection of two conics, given only five points on each?

Proof without words of a simple conjecture about any triangle