Question

http://prntscr.com/92c419

Answer 1

Have you seen the Intercept theorem at school ?

Answer 2

no.

Answer 3

Well, it basically says that:
In triangle ABC, let M be a point in AB and N a point in AC. If MN is parallel to BC then : \[\frac{ AM }{ AB }=\frac{ AN }{ AC }=\frac{ MN }{ BC }\] You can use here in triangle AHC.

Answer 4

So what do i do?

Answer 5

What does D represent in segment AC ?

Answer 6

side? angle?

Answer 7

No, I mean the point D.

Answer 8

I hope you get this when you're back:
D is the midpoint of AC and G is the midpoint of AH, hence according to the Intercept theorem (or Thales) \[\frac{ AG }{ AH }=\frac{ AD }{ AC }=\frac{ GD }{ HC }= \frac{ 1 }{ 2 }\] Meaning GD is half the length of HC.