Brain Easier

Geometry Level 3

$A$ and $B$ are two fixed points. If the vertex $C$ of $\triangle ABC$ moves such that $\cot (A)+ \cot (B)=k$ , the the locus of $C$ is $\text{\_\_\_\_\_\_\_\_\_\_}$ .

Parallel to

AB

Perpendicular to

AB

1 solution

Marta Reece
Aug 20, 2017

$\cot DAC+\cot DBC=\dfrac{AD}{DC}+\dfrac{DB}{DC}=k=$ constant

Which simplifies to $AD+DB=k\times DC$

But $AD+DB=AB$ , which is constant.

So $DC$ is also constant and the motion is along a line parallel to $AB$ .

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