Question

Where is the orthocenter of obtuse triangle CDE located? Find GD.

A.outside of the triangle; GD = 5
B.inside the triangle; GD = 5
C.outside of the triangle; GD = 7
D.inside the triangle; GD = 7

Answer 1

Is there a figure?

Answer 2

We know that EGC is the supplementary angle of CGD, so:
∠EGC=180∘−∠CGD=180∘90∘=90∘
But we are also told that:
EGC=(5x+55)∘
So we can say:
(5x+55)∘=90∘5x+55=905x=90−55=35x=355=7
So:
GD=2x−9=2⋅7−9=14−9=5

Answer 3

Also, for obtuse triangles the orthocenter will be outside the triangle:
http://www.mathopenref.com/triangleorthocenter.html

Answer 4

almost but still good