3
votes
Proving that the trajectory of point $P$ such that $\frac{PF_1}{PF_2} = a$ is a circle of Apollonius
Let $G_1$ be point which lies on line segment $F_1F_2$ such that $\frac{F_1G_1}{F_2G_1}=a$ which means that $PG_1$ is the internal angle bisector of $\triangle PF_1F_2$.
Similarly, Let $G_2$ be point ...
- 9,920
1
vote
Proving that the trajectory of point $P$ such that $\frac{PF_1}{PF_2} = a$ is a circle of Apollonius
I'll change notation to simplify typesetting.
Treating the points as complex numbers, we can write the relation between the moving point $z$ and the two fixed points $A$ and $B$ as
$|\frac{z-A}{z-B}| =...
- 5,535
1
vote
Accepted
For which integer n, is there a circle inscribing n gridpoints
I'll do my best to explain the solution given on the link you referenced. The first step is to consider the set $S$ of all lines that are perpendicular bisectors to $2$ integer points. The main ...
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