Tag: mid-point theorem and its converse

D,E,F are midpoints of sides BC, CA and AB of $\Delta ABC$. If perimeter of $\Delta ABC$ is 12.8 cm, then perimeter of $\Delta DEF$ is :

If A, B and C are the midpoint of the sides PQ, QR and PR of $\triangle $PQR respectively, then the area of $\triangle $ABC equals if area of $\triangle PQR$ is $4$ units

The sides $AB, BC$ and $CA$ of a triangle $ABC$ have $3, 4$ and $5$ interior points respectively on them.The number of triangles that can be constructed using these interior points as vertices is 

In $\triangle ABC, D$ and $E$ are the mid point of $\bar {BC}$ and $\bar {AC}$ respectively. $\bar {AD}$ and $\bar {BE}$ intersect each other in $G.A$ line $m$ passing through $D$ and parallel to $\overleftrightarrow { BE } $ intersects $\bar {AC}$ in $K$.
then $AC=4CK$