Exercise

Constructed externally on the sides $AB, AC$ of $△ABC$ are equilateral triangle $ABX$ and $ACY$. If $P, Q, R$ are the mid-ponts of $AX, AY$ and $BC$ respectively, then $△PQR$ is

$ABCD$ is a square. If $P,Q, R$ and $S$ are points on the sides $AB, BC, CD$ and $DA$ respectively, such that $AP=BQ=CR=DS$, then the value of $\angle SPQ$ is equal to

Perpendiculars are drawn from the vertex of the obtuse angles of a rhombus to its sides. The length of each perpendicular is equal to a units. The distance between their feet being equal to $b$ units. Then, the area of the thombus is

ABCD is a parallelogram in which AP and BP are angle bisectors then

Perpendiculars are drawn from the vertex of the obtuse angles of a rhombus to its sides. The length of each perpendicular is equal to $a$ units. The distance between their feet being equal to $b$ units. Then, the area of the rhombus is

In the parallelogram $ABCD$ of the given figure, $\angle PAQ$ is an obtuse angle. Two equilateral triangles $ABP$ and $ADQ$ are drawn outside the parallelogram. Prove that $△CPQ$ is also an equilateral triangle.

If distance of two points is equal from the $Y$-axis and the line joining them is parallel to $X$-axis, then what is the sum of their abscissa?

A road is passing parallel to the diagonal a square field $ABCD$ as shown in the figure below. Two cars are moving in parallel along $AE$ and $CF.$ If the measure of $\angle BAE$ is $20°$ then what is the measure of $\angle BCF?$