KVS MATHS QUIZ 52 (GEOMETRY)

In $\triangle \mathrm{ABC}, \angle \mathrm{B}=90^{\circ},  \mathrm{AD}$ and $\mathrm{CE}$ are the medians drawn from $\mathrm{A}$ and $\mathrm{C}$, respectively. If $\mathrm{AC}=10 \mathrm{~cm}$ and $A D=\sqrt{55} \mathrm{~cm}$, then the length of $\mathrm{CE}$ is:

The length of the base of a right-angled triangle is $40 \mathrm{~cm}$ and its hypotenuse is $41 \mathrm{~cm}$ long. What is its area (in cm) and perimeter (in cm), respectively?

$\triangle \mathrm{ABC}$ is right-angled at $\mathrm{B}$ and $\mathrm{D}$ is a point on $\mathrm{AC}$ such that $\mathrm{BD}$ is perpendicular to $\mathrm{AC}$. If $\mathrm{BD}=6 \mathrm{~cm}$ and $\mathrm{AD}=3 \mathrm{~cm}$, then what will be the length of $\mathrm{AC}$ ?

$A B$ is a chord of a circle with centre $O$ and $P$ is any point on the circle. If $\angle A P B=112^{\circ}$, then what is the measure of $\angle O A B$ ?

Two sides of a triangle are $12.8 \mathrm{~m}$ and $9.6 \mathrm{~m}$. If the height of the triangle is $12 \mathrm{~m}$, corresponding to $9.6 \mathrm{~m}$, then what is its height in $\mathrm{m}$ ) corresponding to 12. $8 \mathrm{~m}$ ?

In $\triangle A B C, \angle B=90^{\circ}, A B=8 \mathrm{~cm}$ and $B C=15 \mathrm{~cm}$. $D$ is a point on $B C$ such that $A D$ bisects $\angle A$. The length (in cm) of $B D$ is:

$\mathrm{ABCD}$ is a cyclic quadrilateral with $\mathrm{AB}$ as a diameter of the circle. If $\angle \mathrm{ADC}=118^{\circ}$, then the measure (in degrees) of $\angle \mathrm{BAC}$ is:

The sides $\mathrm{AB}$ and $\mathrm{AC}$ of $\triangle A B C$ are produced upto points $\mathrm{D}$ and $\mathrm{E}$ respectively. The bisectors of the exterior angles so formed, intersect each other at point I. If $\angle A C B$ is $66^{\circ}$ and $\angle A B C=44^{\circ}$, then what is the measure (in degrees) of $\angle B I C$ ?

The perimeter of an isosceles triangle is $3.6 \mathrm{~m}$ and its base is $30 \mathrm{~cm}$ shorter than each of the equal sides. What is the area (in $\mathrm{m}^{2}$ ) of the triangle?