Question : In $\triangle$ABC, two medians BE and CF intersect at the point O. P and Q are the midpoints of BO and CO, respectively. If the length of PQ = 3 cm, then the length of FE will be:
Option 1: 3 cm
Option 2: 6 cm
Option 3: 9 cm
Option 4: 12 cm
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Correct Answer: 3 cm
Solution :
Given:
PQ = 3 cm
The line joining the mid-points of two sides of a triangle is parallel to the third side and half of the third side.
So from $\triangle$ABC, we get
FE = $\frac{1}{2}×$BC --(1)
and from $\triangle$OBC, we get
PQ = $\frac{1}{2}×$BC --(2)
From equation 1 and 2, we get
FE = PQ = 3 cm
Hence, the correct answer is 3 cm.
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