Question : The perpendicular drawn from the vertices, to the opposite sides of a triangle, meet at the point whose name is:

Option 1: incentre

Option 2: circumcentre

Option 3: centroid

Option 4: orthocentre

Question : The medians CD and BE of a triangle ABC interest each other at O. The ratio $ar(\triangle ODE): ar(\triangle ABC)$ is equal to:

Option 1: $12:1$

Option 2: $4:3$

Option 3: $3:4$

Option 4: $1:12$

Question : If the three medians of a triangle are the same then the triangle is:

Option 1: equilateral

Option 2: isosceles

Option 3: right angled

Option 4: obtuse angle

Question : In triangle ABC, AD BE and CF are the medians intersecting at point G and the area of triangle ABC is 156 cm². What is the area (in cm²) of triangle FGE?

Option 1: 13

Option 2: 26

Option 3: 39

Option 4: 52

Question : In an equilateral triangle ABC, P is the centroid of this triangle. Side of $\triangle A B C$ is $16 \sqrt{3} \ \text{cm}$. What is the distance of point P from side BC?

Option 1: 8 cm

Option 2: 12 cm

Option 3: 9 cm

Option 4: 10 cm