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Maths-

General

Easy

Question

In DABC, AD is the median through A and E is the produced meets in F figure. Then the value of AF is equal to

1/4AC
1/2AC
1/3AC
2/3AC.

The correct answer is: 1/3AC

We should find value of AF in terms of AC
In $Δ A D G$

$E$ is the midpoint of $A D$ and $E F ∣ ∣ D G$

By converse of midpoint theorem we have

$F$ is midpoint of $A G$ and $A F = F G$ .............. $1$

Similarly, in $Δ B C F$

$D$ is the midpoint of $B C$ and $D G ∣ ∣ B F$

$G$ is midpoint of $C F$ and $F G = G C$ .............. $2$

From equations $1$ and $2$

we will get

$A F = F G = G C . . . . . . . . 3$

$A F + F G + G C = A C$

$A F + A F + A F = A C$ ......... from eq $3$

$A F = A C$

$A F = (1 / 3) A C$

Hence AF=(1/3)AC

Related Questions to study

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Hence Choice 1 is correct

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Hence choice 4 is correct

parallel

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Hence choice 2 is correct

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Hence choice 2 is correct

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Hence Choice 2 is correct

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Hence Choice 2 is correct

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