Question

A circle is inscribed in the square as shown in the figure.Clearly the point of intersection of diagonals of square is the center of this circle and also the circle touches square internally at the mid-point ‘F’ Answer the following questions:​

Answer 1

Step-by-step explanation:

Let side of square =a

∴r=

2

a

..(i)

2

a=2R

a=

2

R..(ii)

2r=

2

R

2

R=R

πR

2

πR

2

=(

R

r

)

2

=

2r

2

r

2

=

2

1

Hope its help..

Answer 2

$✩ ✰ \huge{ \boxed{\underline{\bf{\sf{Answer : - }}}}} ✩ ✰$

Let AB be a diameter of a circle with centre O,

and let P be any other point on the circle.

Join the radius PO, and let α = angleA and β = angleB.

The triangles AOP and BOP are isosceles because all radii are equal, so angleAPO = α and angleBPO = β (base angles of isosceles triangles AOP and BOP).

Hence α + β + (α + β ) = 180° (angle sum of triangleAPB)