(x) DEF is the pedal triangle of the equilateral `Delta ABC.` Find `angle BED`.

Find all the angles of an equilateral triangle.

Prove that the Pedal triangle of an equilateral triangle is also an equilateral triangle.

The given figure shows a right angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.

If R_(1) is the circumradius of the pedal triangle of a given triangle ABC, and R_(2) is the circumradius of the pedal triangle of the pedal triangle formed, and so on R_(3), R_(4) …… then the value of sum_(i=1)^(infty) R_(i) , where R (circumradius) of Delta ABC is 5 is

In the figure given below, equilateral triangle ECB surmonunts sqaure ABCD. Find the angle BED represented by x.

In the figure given below, equilateral triangle ECB surmonunts sqaure ABCD. Find the angle BED represented by x.

Equilateral triangle ABC with a side-length of 2 is inscribed in 30^@–60^@-90^@ triangle DEF such that each of its vertices is on a different side of triangle DEF and none of them is coincident with a vertex of triangle DEF. If one side of the equilateral triangle is parallel to the shortest side of triangle DEF, then the area of triangle DEF is

D, E and F are the mid-points of the sides BC, CA and AB, respectively of an equilateral Delta ABC. Show that Delta DEF is also an equilateral triangle.