In the given diagram, $\Delta ABC$ is a right angled triangle in which $m \angle B=90$ and $AB = BC =14\, cm$ Minor sector $BAPC$ is a sector of $\odot( B , BA )$ and semicircle arc $\widehat{ AQC }$ is drawn on diameter $\overline{ AC }$. Find the area of the shaded region. (in $cm^2$)
$90$
$86$
$98$
$104$
The diameter of a circle with area $38.5\,m ^{2}$ is $\ldots \ldots \ldots \ldots m$.
In a circle, the ratio of the areas of two distinct minor sectors is $1: 4 .$ Then, the ratio of the angles at the centre for those minor sectors is $\ldots \ldots \ldots \ldots .$
The length of a diagonal of a square inscribed in a circle with radius $10\, cm$ is $\ldots \ldots \ldots . cm$.
The radius of a circular ground is $56\, m$. Inside it, runs a road of width $7 \,m$ all along its boundary. Find the area of this road. (in $m^2$)
Is the following statement true? Give reasons for your answer.
Area of a segment of a circle $=$ area of the corresponding sector - area of the corresponding triangle.