The length of a diagonal of a square inscribed in a circle with radius $10\, cm$ is $\ldots \ldots \ldots . cm$.

If the radius of a circle is doubled,its area becomes $\ldots \ldots \ldots$ times the area of the original circle.

In the figure,a square is inscribed in a circle of diameter $d$ and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.

The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why?

The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters $36 \, cm$ and $20 \, cm$ is (in $cm$)

The maximum area of a triangle inscribed in a semicircle with diameter $30 \, cm$ is $\ldots \ldots \ldots \, cm^{2}$.