$AB$ 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

The perimeter of a square is double the perimeter of a rectangle. The area of the rectangle is $240 \, cm^2$. What is the area of the square? (in $cm^2$)

In the given figure,there is a large semicircle with diameter $AB = 56 \ cm$. Inside this,there are four smaller identical semicircles with diameters $AE, EF, FG,$ and $GB$ along the diameter $AB$. $A$ circle is inscribed such that it is tangent to the large semicircle and the two middle smaller semicircles. What is the area (in $cm^2$) of the shaded region?

The perimeters of a circle,a square,and an equilateral triangle are the same,and their areas are $C$,$S$,and $T$ respectively. Which of the following statements is true?

$ABCD$ is a trapezium with $AD$ and $BC$ as parallel sides. $E$ is a point on $BC$. The ratio of the area of $ABCD$ to that of $\Delta AED$ is

$ABCD$ is a trapezium in which $AB \parallel CD$ and $AB = 2CD$. If its diagonals intersect each other at $O$,the ratio of the area of triangle $AOB$ and $COD$ is