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If p,q,r denote the three distances from the vertices and `a` is the side of the equilateral triangle
then we have 3(p^4+q^4+r^4+a^4)=(p^2+q^2+r^2+a^2)^2 (try proving yourself)
1)in an equilateral triangle of side a, the distance of a point P from its vertices is given 3.4 and 5 respectively.FIND THE VALUE OF THE SIDE a.
2)On similar ground try to to find the side of a square ABCD such that the distance of apoint p from its vertices A,B,C is 3,4,5 respectively.
3)prove this question by pure geometry.
PROVE THAT ΔABC is equilateral.
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3 Answers
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11Exactly you cannot solve this question by conventional methods and zorro idont get the ans by your identity.
THIS POSTS HEADING IS PURE GEOMETRY AND SO USE ONLY PURE GEOMETRY.