Question

In an equilateral triangle sum of the distances of orthocenter from all the vertices is equal to -
(Where 'R' is the circumradius of triangle)

• A. R
  
• B. 2R
• C. 3R
• D. 4R

Answer 1

The correct option is C

3R

Let the triangle be ABC and the orthocenter be O.
We know that OA = 2RcosA

It is given that triangle is equilateral. So cosA = cos (60°) = $\frac{1}{2}$
And OA = R
Similarly, OB = OC = R
And the sum of them = OA + OB + OC = 3R