Question

If $P$ is a point inside the scalene triangle $ABC$ such that $\Delta APB$, $\Delta BPC$ and $\Delta CPA$ have the same area, then $P$ must be:

• A. In centre of $\Delta ABC$
• B. Circum centre of $\Delta ABC$
• C. Centroid of $\Delta ABC$
• D. Ortho centre of $\Delta ABC$

Answer 1

The correct option is A In centre of $\Delta ABC$

We can't divide a triangle into three parts using the points on the sides of a triangle.

So, we need to take a point inside the triangle to make three triangles from one triangles.

(A centroid of a triangle is the point where the three medians of the triangle meet. A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle.)

Now, to divide an scalene triangle $ABC$ into three triangles $APB,BPC,CPA$ of same area we need to take a point in the centre and that point is called centroid.

Centoid of $△ABC$ is point $P$.

Thus, $P$ must be in centre of $△ABC$.