Tag: mid-point and its converse
Questions Related to mid-point and its converse
In any triangle are the circumcentre, the centroid, the nine point centre and the orthocentro are all collinear ?
Mid-point theorem states that:
In $\Delta ABC$, AB$ =5$cm, $BC=8$cm and $CA=7$cm. If D and E are respectively, the mid-points of AB and BC, then determine the length of DE.
Suppose $ABCD$ is a rhombus. A straight line passing through $C$ meet $AD$ which is produced at $P$ and meet $AB$ produced at $Q$. Therefore if $DP=\dfrac {1}{2}AB$, then find the ratio between $BQ$ and $AB$?
The median $AD$ of the triangle $ABC$ is bisected at $E$, $BE$ meets $AC$ in $F$, then $AF:AC$ is equal to ?
The incentre of the triangle formed by $(0, 0, 0), (3, 0, 0), (0, 3, 0)$.
The mid-points of the sides of a triangle are $D(6,1),E(3,5)$ and $F(-1,-2)$ then vertex opposite to D is
ABC is an isosceles triangle with AB=AC. D,E, F are mid point of sides BC,AB and AC respectively then line segment $A D \perp E F$ and is bisected by it.
Each side of $\triangle ABC$ is 12 units. D is the foot of the perpendicular dropped from A on BC and E is the mid point of AD. The length of BE in the same units is:
In $ABC,E$ and $F$ are mid points of sides $AB$ and $AC$ respectively then $EF // BC$