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

In an equliateral triangle of side 2sqrt3 cm. The find circum-radius.

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

In fig. trianglePQR is an equilateral triangle with points Q(-3,0) and R(3,0). Find the coordinates of the vertex P.

AL, BM and CN are perpendicular from angular points of a triangle ABC on the opposite sides BC, CA and AB respectively. Delta is the area of triangle ABC, (r ) and R are the inradius and circumradius. Radius is the circum circle of Delta LMN is

A uniform conducting wire of length 12a and resistance R is wound up as a current carrying coil in the shape of an equilateral triangle of side a. The coil is connected to a voltage source V_0 . Find the magnetic moment of the coils in each case.

In a triangle ABC, AD, BE and CF are the altitudes and R is the circum radius, then the radius of the circle DEF is

Area of an equilateral triangle is 17300 cm^2 . By taking each vertex of the triangle as centre, a circle is drawn at each vertex. The radius of thecircleis half of the length of the side of an equilateral triangle. Find the area of that portion of the triangle which is not included in the circle. (pi=3.14 and sqrt3=1.73 )

In a circular table cover of radius 32cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in fig. Find the area of the design (shaded region).

Three resistances each of 4 ohm are connected in the form of an equilateral triangle. What is the effective resistance between two corners of the triangle?

If R be circum-radius of DeltaABC, then circum-radius of a pedal Delta is