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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

In the figure shown below, $angle B equals angle C equals 65 to the power of ring operator end exponent$ and $angle D equals 35 to the power of ring operator end exponent$ . Which one of the following is a true statement?

Hence Choice 1 is correct

In the figure shown below, $angle B equals angle C equals 65 to the power of ring operator end exponent$ and $angle D equals 35 to the power of ring operator end exponent$ . Which one of the following is a true statement?

Hence Choice 1 is correct

One of the angles of a triangle is $65 to the power of ring operator end exponent$ . If the difference of other two angles is $25 to the power of ring operator end exponent$ , the largest angle of this triangle has a measure of

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Hence choice 4 is correct

In figure $angle X equals 62 to the power of ring operator end exponent comma angle X Y Z equals 54 to the power of ring operator end exponent$ If YO and ZO are bisectors of $angle X Y Z$ and $angle X Z Y$ respectively of $capital delta X Y Z$ , find $angle Y O Z$

Hence choice 4 is correct

parallel

In figure if $Q T perpendicular P R comma angle T Q R equals 40 to the power of ring operator end exponent$ and $angle S P R equals 30 to the power of ring operator end exponent$ , find x and y.

Hence choice 2 is correct

In figure if $Q T perpendicular P R comma angle T Q R equals 40 to the power of ring operator end exponent$ and $angle S P R equals 30 to the power of ring operator end exponent$ , find x and y.

Hence choice 2 is correct

In Figure. PS is the bisector of $angle Q P R$ and $P T perpendicular Q R$ . Then $angle T P S$ is equal to

Hence Choice 2 is correct

In Figure. PS is the bisector of $angle Q P R$ and $P T perpendicular Q R$ . Then $angle T P S$ is equal to

Hence Choice 2 is correct

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Statement I: Kinetic energy of 'A' on sliding to J will be greater than the kinetic energy of B on falling to M.
Statement II: Acceleration of 'A' will be greater than acceleration of 'B' when both are released to slide on inclined plane. Statement III: Work done by external agent to move block slowly from position B to O is negative

Two identical blocks A and B are placed on two inclined planes as shown in diagram. Neglect air resistance and other friction. Choose the correct statement:

Statement I: Kinetic energy of 'A' on sliding to J will be greater than the kinetic energy of B on falling to M.
Statement II: Acceleration of 'A' will be greater than acceleration of 'B' when both are released to slide on inclined plane. Statement III: Work done by external agent to move block slowly from position B to O is negative

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