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Published on December 28th, 2010 In category Education | Maths

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Problem solving concept- equilateral triangle

Equilateral TriangleAn equilateral triangle has all the sides that equal the included angles are also equal.

These are some important concept on the Geometry that can help to solve the problems in Co-ordinate geometry 

 For a given perimeter the equilateral triangle has the largest area

 For a given area the equilateral triangle has the least perimeter

  • Area (A) of Equilateral triangle is = A  =  [ (square of a Side) x Square root of 3 ] / 4  =
      • Remember all the sides of equilateral triangle are equalEquilateral-Triangle- Distance of a point from vertex
     
  • Perimeter of Equilateral triangle = 3s – S is the side of triangle
  • The radius of the circumscribed circle (the circle touching all the vertex from outside) = R = s x (Square root of 3)/ 3
  • The radius of the inscribed circle  – r = s x (square root of 3) / 6
  • Height of the equilateral triangle = h = s x (square root of 3)/ 2
  • For any point P in the plane, with distances p, q, and t from the vertices A, B, and C respectively , s is the side of triangle

3(p4 + q4 + t4 + s4) = (p2 + q2 + t2 + s2)2

  • For any interior point P in an equilateral triangle, with distances d, e, and f from the sides, d+e+f =  H , the altitude of the triangle, independent of the location of P
  • For any point P on the inscribed circle of an equilateral triangle, with distances p, q, and t from the vertices, s is the side of triangle

16(p4 + q4 + t4) = 11s4     and 4(p2 + q2 + t2) = 5s2 

  • For any point P on the minor arc BC of the circumcircle, with distances p, q, and t from A, B, and C respectively,                              p = q + t and q2 + qt + t2 = a2

  

  • If point N on side BC divides PA into segments PD and DA with DA having length z and PD having length y, thenDistance on a point on minor arc of equilateral triangle
    z= \frac{t^{2}+tq+q^2}{t+q},

    which also equals if tq; and  

    \frac{1}{q}+\frac{1}{t}=\frac{1}{y}.

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