Question

From a point within a triangle segments are drawn to the vertices A necessary and sufficient condition that the three triangles formed have equal areas is that the point be

• A. such that the three angles formed each have a measure of ${120}^{\circ }$
• B. the centre of the inscribed circle
• C. the centre of the circumscribed circle
• D. the intersection of the medians

Answer 1

The correct option is D the intersection of the medians

The triangles formed will have equal areas only in case of an equilateral triangle.This condition is necessary and sufficient. So the three angles formed each have a measure of $120$ degrees. OPTION A is correct.