In an equilateral triangle show that the in-radius and the circum-radius are connected by `r =R/2.`

In a right angles triangle, prove that r+2R=s.

What is the area of an equilateral triangle inscribed in a circle of radius 4cm?

Prove that the area of the circle with radius r is pi r^2

Three identical metal balls, each of the radius r are placed touching each other on a horizontal surface such that an equilateral triangle is formed when centre of three balls are joined. Then where does their centre of mass?

Fill in the blanks so as to make each of the following statements true : The area of the largest triangle that can be inscribed in a semicircle of radius r cm is …………. cm^(2) .

Show that the angles of an equilateral triangle are 60^@ each.

If a, b, c are the side of a right triangle where c is the hypotenuse, prove that the radius of the circle which touches all the side of the triangle is given by r= (a+b-c)/2 .