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Equal Intercept Theorem

With respect ...

Question

With respect to given figure, state true or false
In figure, C is mid-point of the line segment AB. D and E are mid-points of the segments AC and BC respectively. Then $A B = 4. A D$

True

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False

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Solution

The correct option is A True
$C$ is mid-point of the line segment $A B$ .
So, $A C = C B$
$D$ and $E$ are mid-points of the segments $A C$ and $B C$ respectively.
So, $A D = D C a n d C E = E B$
Since, $A C = A D + D C = A D + A D = 2 A D$
$C B = A C = 2 A D$
Now,
$A B = A C + C B = 2 A D + 2 A D = 4 A D$
So, $A B = 4 A D$

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