Centroid of a Triangle

Q. Match the following points of concurrency with their respective names.

1. Orthocenter
2. Centroid
3. Incenter

Q. The of a triangle is the point where the three medians coincide.

Q. If Y is the centroid of the triangle $△MNO,$ find the medians.

1. MR
2. TQ
3. TO
4. PS

Q. Choose the correct option regarding the triangle $△XYZ.$

1. P is the circumcentre of the triangle.
2. P is the centroid of the triangle.
3. Q is the circumcentre of the triangle.
4. Q is the centroid of the triangle.

Q. The line SR passes through the centroid of the given triangle and meets the triangle at S on one side and the vertex R on the other side. Given PS = $2x$ and SQ = $4x-3$. Find the value of $x.$

1. $1$ unit
2. $1.5$ unit
3. $3$ unit
4. Insufficient data.

Q. If you are looking at a triangle where the orthocenter, the centroid and the circumcenter lie at the same point, what type of triangle are you looking at?

1. Equilateral triangle
2. Right-angled triangle
3. Isosceles triangle
4. Scalene triangle

Q. If you are looking at a triangle where the orthocenter, the centroid and the circumcenter lie at the same point, what type of triangle are you looking at?

1. Scalene triangle
2. Isosceles triangle
3. Right-angled triangle
4. Equilateral triangle

Q. Is it necessary that when two median meet at a point then the third median meet at the same point? Answer in Yes/No.

Q. Which among the following is true for a triangle?

1. The point of intersection of medians is known as orthocentre.
2. A median is line joining the vertex to the midpoint of the opposite side.
3. A median always lies outside the triangle.
4. A centroid always lies outside the triangle.