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Olympiad workbook

Exam: Olympiad workbook
Subject: IOQM
Chapter: Properties of Triangles

Olympiad workbook · IOQM · Properties of Triangles

In a triangle A B C , let E be the midpoint of A C and F be the...

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

.

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

Correct answer

10

Step-by-step solution

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

Let

B E=6 x

C F=6 y

\frac{\operatorname{area}(G Y Z)}{\operatorname{area}(G B C)}=

\left(\frac{1}{4}\right)^2 \operatorname{Area}(G B C)=16(

area of

G Y Z)

area of

G B C=\frac{1}{3}

of

\operatorname{area}(A B C)=\frac{480}{3}=160

area of

G Y Z=10

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