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Olympiad workbookIOQMProperties of Triangles

In a triangle A B C , let E be the midpoint of A C and F be the midpoint of A B . The medians B E and C F intersect at G . Let Y and Z be the midpoints of B E and C F respectively. If the area of triangle A B C is 480 , find the area of triangle C Y Z .

Correct answer

10

Step-by-step solution

Let B E=6 xC F=6 y area (G Y Z) area (G B C) = ( 1 4 )^2 Area (G B C)=16( area of G Y Z) area of G B C= 1 3 of area (A B C)= 480 3 =160 area of G Y Z=10

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