Congruent parts

Geometry Level 3

In triangle $ABC$ above, if $AE=EC$ and $AD=DG=GB$ , find $\frac {CF}{FG}$ . If you've come to the conclusion that the value cannot be derived, type in 0.

The answer is 3.

2 solutions

展豪張
Dec 2, 2015

Apply Menelaus' theorem
$\dfrac{CE}{EA}\cdot\dfrac{AB}{BG}\cdot\dfrac{GF}{FC}=-1$
$\dfrac 11\cdot\dfrac 3{-1}\cdot\dfrac{GF}{FC}=-1$
$\dfrac{CF}{FG}=3$

Thanx d bro.

Shubham Ghosh - 5 years, 6 months ago

How did you derive BG to -1 ?

Tim Kristian Llanto - 5 years, 6 months ago

BG and AB are in opposite direction, so they must be of different sign.

展豪張 - 5 years, 6 months ago

Curtis Clement
Nov 30, 2015

Using a point mass system: $\ M_{A}=M_{C} = 1$ so $\ M_{E} = M_{A}+M_{C} = 2$ Now $\ AG: GB = M_B : M_A = 2:1$ $\therefore\ M_A = 2$ $\ M_G = M_A + M_B = 3$ $\therefore\frac{CF}{FG} = \frac{M_G}{M_C}= 3$

What is point mass?

Shubham Ghosh - 5 years, 6 months ago

You imagine that you have a mass at a point and that you want the weights to balance on the lines, in the same way that weights balance on levers. If you're still not sure, see the Barycentric Coordinates Wiki on Brilliant

Curtis Clement - 5 years, 6 months ago

Congruent parts

The answer is 3.

2 solutions

0 pending reports