This will be my first question :-)
Let $\mathcal{D}_1$ and $\mathcal{D}_2$ two concurrent lines, and $F$ a point in the plane, and $H$ and $G$ its images by the symmetries of axis $\mathcal{D}_1$ and $\mathcal{D}_2$.
1) ( I solved this one, but I'm attaching it if it is somehow related ) : Find the locus of the point $F$ which satisfies $HG=\lambda$ ( where $\lambda > 0$ ).
Easy : If we call $E$ the intersection of the two lines and $\alpha$ the angle between them, we find that it is the circle of center $E$ and radius $\frac{\lambda}{2\sin \alpha}$.
2) Same question but this time we fix $FG+FH$ and not $HG$, in other words, the equation becomes $FG+FH=\lambda$.
Here I don't have any idea. First I conjectured that it might be a circle of center $E$ too, but later I found out that it is impossible...
Any hints please ? I'm not good in geometry, in fact, I'm doing this kind of exercises this summer in order to level up a little :-)
Thank you !
Here's a construction I did with GeoLabo :