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Two circles of radii $10\ cm$ and $8\ cm$ intersect each other, and the length of the common chord is $12\ cm$. Find the distance between their centres.
In a quadrilateral $ABCD$, show that $(AB + BC + CD + DA) > (AC + BD)$.
$ABC$ is a triangle. The bisector of the exterior angle at $B$ and the bisector of $\angle\text{C}$ intersect each other at $D$. Prove that $\angle\text{D}=\frac{1}{2}\angle\text{A}.$
Ravish tells his doughter Aarushi, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be".. lf present ages of Aarushi and Ravish are $x$ and $y$ years respectively, represent this situation algebraically as well as graphically.
In $\triangle\text{ABC},$ if $3\angle\text{A}=4\angle\text{B}=6\angle\text{C},$ calculate $\angle\text{A},\angle\text{B}$ and $\angle\text{C}.$
The total surface area of a cylinder is $462\ cm^2$. Its curved surface area is one-third of its total surface area. Find the volume of the cylinder.
The radius of the base and the height of a cylinder are in the ratio $2 : 3$. If its volume is $1617cm^3$, find the total surface area of the cylinder.
In the given figure, $ABCD$ is a cyclic quadrilateral in which $\angle\text{BAD} = 75^\circ,\ \angle\text{ABD} = 58^\circ$ and $\angle\text{ADC} = 77^\circ, AC$ and $BD$ intersect at $P.$ Then, find $\angle\text{DPC}.$
In the adjoining figure, $\text{ABCD}$ is a parallelogram in which $\angle\text{BAO}=35^{\circ},\angle\text{DAO}=40^{\circ}$ and $\angle\text{COD}=150^{\circ}.$ Calculate
$i. \angle\text{ABO},$
$ii. \angle\text{ODC},$
$iii. \angle\text{ACB},$
$iv. \angle\text{CBD}.$
Draw a histogram to represent the following data:
Class interval
$10-14$
$14-20$
$20-32$
$32-52$
$52-80$
Frequency
$5$
$6$
$9$
$25$
$21$