Question

Could you help me find the measurement of these please? Find the measurement of GD, BG, FC, BF

Answer 1

Given data:

The given triangle.

If G is the incentre of the given circle then,

GD=GE=GF

In triangle GDC.

`\begin{gathered} GC^2=GD^2+CD^2 \\ 37^2=GD^2+35^2 \\ GD^2=144 \\ GD=12 \end{gathered}`

It means GD=GE=GF=12.

In triangle BEG.

`\begin{gathered} BE^2+GE^2=BG^2 \\ 6^2+12^2=BG^2 \\ BG^2=180 \\ BG=\sqrt[]{180} \end{gathered}`

In triangle FGC.

`\begin{gathered} FG^2+FC^2=GC^2 \\ 12^2+FC^2=37^2 \\ FC^2=1225 \\ FC=35 \end{gathered}`

Similarly BF=6, as triangle BEG is congruent ot the triangle BFG.

Thus, GD=12, BG=(180)^(1/2), FC=35, and BF=6.