Question

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.

• A. only 1,2,3,4
• B. only 1,4
• C. only 1,4,5
• D. All 1,2,3,4,5

Answer 1

The correct option is B

only 1,4

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

Centroid G of the triangle ABC, divides the median AD in the ration 2:1 and coordinate of G (Centroid)

$X=\frac{x_1+x_2+x_3}{3},Y=\frac{y_1+y_2+y_3}{3}$
Statement 1 is correct
2. Incentre of a triangle is the point of concurrency of internal bisectors of the angles of the triangle

Statement 2 is wrong
3. Circumcentre is the centre of circle passing through the vertices 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.
Statement 4 is correct
5.
Excentre of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of its sides.
So, statement 5 is wrong
ONLY statement 1 and 4 are correct