A line drawn through the midpoint of one side of a triangle parallel to another side intersects the third side. In what ratio the third side is divided?

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1:2

1:3

1:1

2:1

answer is C.

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Detailed Solution

Given that, a line drawn through the midpoint of one side of a triangle parallel to another side intersects the third side.

Question Image

We know Basic proportionality theorem (BPT), says that if a line is drawn parallel to one side of a triangle that intersects the other two sides in distinct points, then the other two sides are divided in the same ratio.
In

Δ A B C

, as D is the midpoint of AB,

A D D B = 1

………[1]
Now given that DE||BC, using BPT we get

A D D B = A E E C

From [1], we get

A E E C = 1

⇒ A E = E C

The parallel line bisects the third line.
Hence the ratio in which it is divided is 1:1.
Therefore, the correct option is 3.

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