The largest and the second largest angles of a triangle are in the ratio of $4:3$. The smallest angle is half the largest angle. What is the difference between the smallest and the largest angles of the triangle? (in $^o$)

$AB$ and $CD$ are two parallel chords of a circle lying on the opposite side of the centre and the distance between them is $17 \, cm$. The lengths of $AB$ and $CD$ are $10 \, cm$ and $24 \, cm$ respectively. The radius (in $cm$) of the circle is

Find the perimeter and area of the shaded portion of the adjoining diagram.

In the given figure,$PQR$ is a triangle and quadrilateral $ABCD$ is inscribed in it. Given $QD = 2 \text{ cm}$,$QC = 5 \text{ cm}$,$CR = 3 \text{ cm}$,$BR = 4 \text{ cm}$,and $PB = 6 \text{ cm}$. What is the area (in $\text{cm}^2$) of the quadrilateral $ABCD$?

The area of a square is $196 \, cm^2$. Its side is half the radius of a circle. The circumference of the circle is equal to the breadth of a rectangle. If the perimeter of the rectangle is $712 \, cm$,what is the length of the rectangle? (in $cm$)

If '$x$' is the median (altitude) of an equilateral triangle,then its area is?