Question : The intersection point of the medians of a triangle is called:

Option 1: Orthocentre

Option 2: Incentre

Option 3: Circumcentre

Option 4: Centroid

Question : What are the coordinates of the centroid of a triangle whose vertices are A (2, 5), B (–4, 0), and C (5, 4)?

Option 1: (–1, 3)

Option 2: (1, 3)

Option 3: (1, –3)

Option 4: (–1, –3)

Question : Let $\text{AX}\perp \text{BC}$ of an equilateral triangle $\text{ABC}$. Then the sum of the perpendicular distances of the sides of $\triangle \text{ABC}$ from any point inside the triangle is:

Option 1: Equal to $BC$

Option 2: Equal to $AX$

Option 3: Less than $AX$

Option 4: Greater than $AX$

Question : An equilateral triangle has sides of 18 cm each. The ratio of the inradius to circumradius of the triangle is:

Option 1: 2 : 1

Option 2: 3 : 2

Option 3: 3 : 4

Option 4: 1 : 2

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