In `/_\ABC`,a/cosA=b/cosB=c/cosC.Show that the triangle is equilateral.

In triangle ABC, a sin A= b sin B. Show that the triangle is isosceles.

The vertices of a triangle are (a, 0), (-a, 0) and (0, sqrt(3a)) . Show that the triangle is equilateral.

If in triangle ABC , (a^2+b^2)sin(A-B)=(a^2-b^2)sin(A+B) ,show that the triangle is either'isosceles or right angled.

If the measures of the medians of a triangle are equal then prove that the triangle is equilateral.

If cot (A/2)=(b+c)/a.show that /_\ABC is right angled.

If sinA =cosB , then show that A+B=90 .

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

The area of an equilateral triangle ABC is 17320.5cm^2 .With each vertex of the triangle as center,a circle is drawn with radius equal to half the length of the side of the triangle(seeFig.12.28).Find the area of the shaded region.(use pi=3.14 and sqrt3=1.73205 )

All____ triangles are similar. (isosceles, equilateral)

Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angle triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides.