SOLUTION: Medians AD, BE, and CF of triangle ABC meet at G, EF intersects AD at H, and AD=18. Find GH. Diagram: https://imgur.com/5pOXsWz

Question 1149672: Medians AD, BE, and CF of triangle ABC meet at G, EF intersects AD at H, and AD=18. Find GH.
Diagram: https://imgur.com/5pOXsWz
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
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Segment FE is the mid line in triangle ABC; therefore, line FE is parallel to BC.


Hence, triangles ABC and AFE are similar with the similarity coefficient 2 (from larger to smaller).


From it, you easily deduce that the length of AG is half of the length of AD; thus the length of AG is 18/2 = 9.


The intersection point divides the medians in proportion 2:1; therefore, the length of GD is 1/3 of the length AD;

thus the length of GD is 6 units.


It implies that the length of GF is  9-6 = 3 units.    ANSWER

Solved.

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