$K$ is any point on side $\overline{BC}$ of triangle $\triangle ABC$ . Find the length of the common chord of the nine-point circle of triangle $\triangle ABK$ and triangle $\triangle AKC$ if $\overline{AK} = 10$.
Find length of common chord of nine point circle.
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geometry
euclidean-geometry
geometric-construction
1 Answers
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The common chord is just the segment joining the midpoint of $AK$ with the projection $H_A$ of $A$ on $BC$. Since $\widehat{K H_A A}=90^\circ$, the length of the common chord is just $\color{red}{5}$.
