In any triangle: Formulas

  • In an isosceles triangle , the perpendicular from the vertex to the base or the angular bisector from vertex to base bisects the base.
  • In any triangle the angular bisector of an angle bisects the base in the ratio of the other two sides.

Let a be the side of an equilateral triangle . then if three circles be drawn inside
this triangle touching each other then each’s radius = a/(2*(root(3)+1))

  • In any triangle

a/SinA = b/SinB =c/SinC=2R , where R is the circumradius

cosC = (a^2 + b^2 – c^2)/2ab

sin2A = 2 sinA * cosA
cos2A = cos^2(A) – sin^2 (A)


  • In any triangle

a=b*CosC + c*CosB
b=c*CosA + a*CosC
c=a*CosB + b*CosA

  • Area of a triangle

1/2*base*altitude = 1/2*a*b*sinC = 1/2*b*c*sinA = 1/2*c*a*sinB = root(s*(s-a)*(s-b)*(s-c)) where s=a+b+c/2
=a*b*c/(4*R) where R is the CIRCUMRADIUS of the triangle = r*s ,where r is the inradius of the triangle .

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