Answer:
HC=[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Let HC=x, it is given that AH=3HC, then AH=3x.
Since, from the given figure, ΔABC is similar to ΔBHC and ΔABC is similar to ΔABH.
Therefore, ΔABH is similar to ΔBHC, hence using the similarity conditions,
[tex]\frac{HC}{BH}=\frac{BH}{AH}[/tex]
[tex]\frac{x}{3}=\frac{3}{3x}[/tex]
[tex]3x^{2}=9[/tex]
[tex]x^{2}=3[/tex]
[tex]x=\sqrt{3}[/tex]
Hence, HC=[tex]\sqrt{3}[/tex].
