2D Geometrical Shapes

If $O$ is the in-centre of $∆\mathrm{ABC}$ and if $\angle BOC=120°$, then find the measure of $\angle BAC$.

If in the triangles $ABC$ and $EDF$, $\angle A$ is equal to $\angle E$, both are equal to $40°$, $AB:ED=AC:EF$ and $\angle F$ is $65°$, then angle $B$ is:

If one angle is the sum of the other two angles and the difference between the greatest and least angles is $60°$, then the formed triangle is called _____.

The amount of space occupied by a three dimensional objects is called its_______?

If $S$ is the circumcentre of $∆\mathrm{ABC}$ and $\angle A=50°$, then find the value of $\angle BCS$.

A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?

If each angle of triangle is in the ratio of $2:3:5$, then find the largest angle of triangle.

If $\mathrm{ABCD}$ is a rhombus then ${\mathrm{AB}}^2+{\mathrm{BC}}^2+{\mathrm{CD}}^2+{\mathrm{AD}}^2$ is equal to (where diagonal bisect at $\mathrm{O}$) ______

An isosceles triangle ABC is right-angled at B. D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the sides AB and AC respectively of triangle ABC. If$AP=a \mathrm{cm}, AQ=b \mathrm{cm}$and $\angle BAD=15°, \sin 75° =$ _____.

$I$ is the incentre of a $∆ABC$. If $\angle ABC=65°$ and $\angle ACB=55°$, then the value of $\angle BIC$ is:

The opposite angles of a parallelogram are __________________.

In a $∆ABC$, $\angle B=60°$, $\angle C=40°$ and $AD$ and $AE$ are respectively the bisector of $\angle A$ and the perpendicular drawn to $BC$. The $\angle EAD$ is:

In $\mathrm{\Delta ABC}$, the medians $\mathrm{AD}, \mathrm{BE} \& \mathrm{CF}$ intersect each other at the point $\mathrm{G}$. If the area of $\mathrm{\Delta ABC}$ is $36 {\mathrm{cm}}^2$, then the area (in sq. cm) of the quadrilateral $\mathrm{BDGF}$  is ______

If a square ABCD is inscribed in a circle and AB =$4 cm$., then the radius of circle is-

The wheel of a motor car makes $1000$ Resolutions in moving $440 meter$. The diameter (in meter) of the wheel is -

A polygon with minimum number of sides is:

$O$ is the orthocentre of a $∆ABC$. If $\angle BOC=110°$, $\angle BAC$ is equal to:

If the length of a chord of a circle at a distance of $4$cm from the centre is $6$cm, then the diameter of the circle is-

Let $∆\mathrm{ABC}$ be an equilateral triangle. Let $BE\perp CA$ meeting $CA$ at $E$, then find the value of $(A{B}^2 +B{C}^2 +C{A}^2)$.

One chord of a circle is known to be $10.1$$cm$. The radius of this circle must be: