(C) In $\Delta ABC$,$E$ is the midpoint of $\overline{AC}$.Therefore,$AC = 2EC$ $(1)$.In $\Delta BEC$,line $DK$ passes through the midpoint $D$ of $\o

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(C) In $\Delta ABC$,$E$ is the midpoint of $\overline{AC}$.Therefore,$AC = 2EC$ $(1)$.In $\Delta BEC$,line $DK$ passes through the midpoint $D$ of $\overline{BC}$ and is parallel to $\overline{BE}$.By the Converse of the Midpoint Theorem,$K$ is the midpoint of $\overline{EC}$.Therefore,$EC = 2EK$ $(2)$.Substituting $(2)$ into $(1)$,we get $AC = 2(2EK) = 4EK$.

Class 10 Mathematics Triangles Mix Examples - Triangles

Medium

In $\Delta ABC$,$D$ and $E$ are the midpoints of $\overline{BC}$ and $\overline{AC}$ respectively. $\overline{AD}$ and $\overline{BE}$ intersect at $G$. Line $m$ passing through $D$ and parallel to $\overline{BE}$ intersects $\overline{AC}$ at $K$. Then,$AC = \ldots$ (in $EK$)

A
$2$
B
$3$
C
$4$
D
$6$

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Mix Examples - Triangles

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AB = 10.8$,$MB = 4.5$ and $AC = 4.8$,find $AN$.

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In $\Delta ABC$,$\overline{AD}$ is a median. If $AB = 8$ and $AD = BD = 8.5$,find $AC$.

Medium

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In $\Delta XYZ$,$\overline{XN}$ is a median. If $XY^2 + XZ^2 = 200$ and $XN = 8$,find $YZ$.

Medium

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In $\Delta ABC$,$m\angle B = 90^\circ$. If $AB = 12$ and $BC = 5$,then $AC = \dots$

Medium

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As shown in the adjoining diagram,$\angle B$ is an obtuse angle and $\overline{AM}$ is an altitude in $\Delta ABC$. Prove that $AC^{2} = AB^{2} + BC^{2} + 2 \cdot BC \cdot BM$.

Medium

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In $\Delta ABC$,$D$ and $E$ are the midpoints of $\overline{BC}$ and $\overline{AC}$ respectively. $\overline{AD}$ and $\overline{BE}$ intersect at $G$. Line $m$ passing through $D$ and parallel to $\overline{BE}$ intersects $\overline{AC}$ at $K$. Then,$AC = \ldots$ (in $EK$)

Similar Questions

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AB = 10.8$,$MB = 4.5$ and $AC = 4.8$,find $AN$.

In $\Delta ABC$,$\overline{AD}$ is a median. If $AB = 8$ and $AD = BD = 8.5$,find $AC$.

In $\Delta XYZ$,$\overline{XN}$ is a median. If $XY^2 + XZ^2 = 200$ and $XN = 8$,find $YZ$.

In $\Delta ABC$,$m\angle B = 90^\circ$. If $AB = 12$ and $BC = 5$,then $AC = \dots$

As shown in the adjoining diagram,$\angle B$ is an obtuse angle and $\overline{AM}$ is an altitude in $\Delta ABC$. Prove that $AC^{2} = AB^{2} + BC^{2} + 2 \cdot BC \cdot BM$.

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