2D Geometrical Shapes

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

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

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:

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

In the given figure $O$ is the Centre of a circle $OM=3 cm and AB=8 cm$. Find the radius of the circle?

The lengths of three medians of a triangle are $9 \mathrm{cm}$, $12 \mathrm{cm}$ and $15 \mathrm{cm}$. The area (in $\mathrm{sq}. \mathrm{cm}.$) of the triangle is:

If the circumcentre of a triangle lie on the side whose adjacent angles are $45°$ each, then find the other two sides if the radius of the circumcircle is $15 \mathrm{cm}$?

In $∆ABC$, $D$ and $E$ point in such that $DE\parallel BC$ and $AD:BD=2:3$, then find the ratio of the area of parallelogram $DECB$ and $∆ABC$:

If the points $A(4,3)$and $B(x,5)$are on the circle with Centre$O(2,3)$. Find the value of $x$.

In a $\Delta ABC$, $\angle A:\angle B:\angle C=2:3:4$. If a line $CD$ drawn parallel to $AB$, then the measure of $\angle ACD$ is:

In an obtuse angle $∆\mathrm{ABC}$, $O$ is orthocenter, $\angle BOC$ is $54°$, then find the value of $\angle BAC$.

In $∆ABC$, $D$ and $E$ are points on $AB$ and $AC$ respectively such that $DE\parallel BC$ and $DE$ divides the $∆ABC$ in to two parts of equal areas. Then ratio of $AD$ and $BD$ is:

$O$ is the circumcentre of $∆ABC$. If $\angle BAC=85°$ and $\angle BCA=55°$, then $\angle OAC$ is equal to:

The vertical angles of two isosceles triangles are same and the ratio of their areas is $9:16$. Then the ratio of their heights is:

In a right-angled $∆ABC$, right angle at $A$, if $AD\perp BC$ such that $AD=p$. If $BC=a$, $CA=b$ and $AB=c$, then which relation is true?

In $∆\mathrm{ABC}$, $AD$ is the angle bisector of $\angle BAC$. If $AB = 2.8 \mathrm{cm}, AC = 4.9 \mathrm{cm}, CD = 2.1 \mathrm{cm}$ , what is the length of $BD$?

In a trapezium $ABCD$, if $AB\parallel CD$,then $A{C}^2 + B{D}^2$ is equal to -

If the median drawn on the base of a triangle is half its base, the traingle will be :

For the $∆\mathrm{ABC}$ is an isosceles triangle and $AB = AC$ and $D$ is a point on $AC$ so that $BD = BC$. If $\angle ABD=\angle CBD$, then find the angle $\angle BAC$.

With vertices of a triangle $ABC$ as centres, three circles are drawn, each touching the other two externally. If the sides of the triangle are $9 \mathrm{cm}$, $7 \mathrm{cm}$ and $6 \mathrm{cm}$, then what will be the radii of the circles?