# Centroid of a Triangle

## Trending Questions

**Q.**

An equilateral triangle of side $9\mathrm{cm}$ is inscribed in a circle then the radius of the circle is?

**Q.**If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the origin, then a3+b3+c3 is equal to

- abc
- 0
- a+b+c
- 3abc

**Q.**

The vertices of a triangle are $(6,0),(0,6)$ and $(6,6)$. The distance between its circumcenter and centroid is

$2$

$\sqrt{2}$

$1$

$2\sqrt{2}$

**Q.**

If G be the centroid of a triangle ABC, prove that :

AB2+BC2+CA2=3(GA2+GB2+GC2)

**Q.**

If a vertex of a triangle is $(1,1)$ and the mid-points of two sides through the vertex are $(-1,2)$ and $(3,2)$, then the centroid of the triangle is

$(1,7/3)$

$(1/3,7/3)$

$(-1,7/3)$

$(-1,7/3)$

**Q.**If in an equilateral triangle ABC, AD is median and in triangle ABD, AE is median, then AB square: AE square will be_________ .

**Q.**Which of the following statements is / are correct statements?

1. Centroid of a triangle is the point of concurrency of medians.

2. Incentre of a triangle is the point of concurrency of perpendicular bisectors of the sides of the triangle.

3. Circumcentre of a triangle is the point of concurrency of internal bisectors of the angles of the triangle.

4. Orthocentre of a triangle is the point of concurrency of altitudes of the triangle drawn from one vertex to opposite side.

5. A triangle can have only one excentre.

only 1, 2, 3, 4

only 1, 4

only 1, 4, 5

All 1, 2, 3, 4, 5

**Q.**In △ABC , G(-4, -7) is the centroid. If the coordinates of A and B are (-14, -19) and (3, 5) respectively, then find the co-ordinates of C.

- (-2, -7)
- (1, 7)
- (-1, -7)
- (-1, 7)

**Q.**

Let $A(4,2),B(6,5)$and $C(1,4)$ be the vertices of $\u2206ABC$.

(i) The median from $A$ meets $BC$ at $D$. Find the coordinates of point $D$.

(ii) Find the coordinates of the point $P$ on $AD$ such that $AP:PD=2:1$.

(iii) Find the coordinates of point $Q$ and $R$ on medians $BE$ and $CF$ respectively such that $BQ:QE=2:1$ and $CR:RF=2:1$.

(iv) What do you observe? [Note : The point which is common to all the three medians is called the centroid and this point divides each median in the ratio $2:1$].

(v) If $A({x}_{1},{y}_{1}),B({x}_{2},{y}_{2})$ and $C({x}_{3},{y}_{3})$ are the vertices of triangle $ABC$, find the coordinates of the centroid of the triangle.

**Q.**In triangle ABC, the median from A is given perpendicular to the median from B. If BC=7cm and AC=6cm, then the length of AB is?

**Q.**Question 7 (v)

Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC.

(e) If A(x1, y1), B(x2, y2) and C(x3, y3) are the vertices of triangle ABC, find the coordinates of the centroid of the triangle.

**Q.**

Two vertices of a triangle are $(-1,4)$ and $(5,2)$. If the centroid is $(0,-3)$ then find the third vertex.

**Q.**If the centroid of the triangle formed by (7, x), (y, −6) and (9, 10) is at (6, 3), then (x, y) is :

- (5, 2)
- (3, 1)
- (4, 0)
- (1, 3)

**Q.**

The in-centre of a triangle with vertices $(1,\sqrt{3})$, $(0,0)$, and $(2,0)$ is

$\left(1,\frac{1}{\sqrt{3}}\right)$

$\left(1,\frac{2}{\sqrt{3}}\right)$

$\left(1,\frac{\sqrt{3}}{2}\right)$

None of these

**Q.**In a triangle, centroid is the point of intersection of

- altitudes.
- perpendicular bisector.
- medians.
- angular bisector.

**Q.**

If $G$ be the centroid of a triangle $ABC$, prove that $A{B}^{2}+B{C}^{2}+A{C}^{2}=3\left(G{A}^{2}+G{B}^{2}+G{C}^{2}\right)$.

**Q.**A(h, -6) , B(2, 3) and C(-6, k) are co-ordinates of vertices of a triangle whose centroid is G(1, 5). What is the values of (h - k)?

- -11

**Q.**Two vertices of a triangle are (3, −5) and (−7, 4), If its centroid is (2, 1), find the third vertex.

**Q.**

Which of the points are points of trisection of A(2, -2) and B(-7, 4)?

**Q.**If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the origin, then a3+b3+c3 is equal to

- abc
- 0
- a+b+c
- 3abc

**Q.**If the centroid of the triangle formed by (7, x), (y, −6) and (9, 10) is at (6, 3), then (x, y) is :

- (5, 2)
- (3, 1)
- (4, 0)
- (1, 3)

**Q.**In $\u2206$PQR, $\angle $Q = 90$\xb0$, seg QM is the median. PQ

^{2}+ QR

^{2}= 169. Draw a circumcircle of $\u2206$PQR.

**Q.**Find the centroid of the triangle whose vertices are A(4, −6), B(3, −2) and C(5, 2)

**Q.**

If a vertex of a triangle is (1, 1) and the mid-points of the two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is _____.

(−1, 73)

(1, 73)

(−13, 73)

(13, 73)

**Q.**

If the coordinates of the mid points of the sides of a triangle are (1, 1), (2, – 3) and (3, 4) Find its centroid. [4 MARKS]

**Q.**

Two vertices of a triangle are (3, –5) and (–7, 4). If its centroid is (2, –1). Find the third vertex.

(10, -3)

(12, -2)

(10, -2)

(9, -2)

**Q.**Find the centroid of triangle A(2, 2), B(1, 7), C(3, 0)

**Q.**Find the centroid of the triangle formed by the point (a, b), (b, c), (c, a) at the origin then find the value of a

^{3 }+ b

^{3}+ c

^{3.}

**Q.**ABC is a triangle in a plane with vertices A(2, 3, 5), B(−1, 3, 2) and C(λ, 5, μ). If the median through A is equally inclined to the coordinate axes, then the value of (λ3+μ3+5) is:

- 1348
- 1077
- 1130
- 676

**Q.**Two vertices of a triangle are (3, -5) and (-7, 4). If its centroid is (2, -1), find the third vertex.