Match the following.
$(1)$ Orthocentre (A) The point of intersection of the perpendicular bisectors of the sides of a triangle.
$(2)$ Centroid (B) The point at which the three angle bisectors of a triangle meet.
$(3)$ Circumcentre (C) The point at which the altitudes of a triangle meet.
$(4)$ Incentre (D) The point at which the medians of a triangle meet.

1 C, 2 D, 3 A, 4 B

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1 A . 2 B . 3 C, 4 D

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1 B, 2 C, 3 D, 4 A

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1 D, 2 A, 3 B, 4 C

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Solution

The correct option is A $1 C, 2 D, 3 A, 4 B$
Point of intersection of all the altitudes is Orthocentre.
Point of intersection of all the medians is Centroid.
Point of intersection of all the perpendicular bisectors is Circumcentre.
Point of intersection of all the angle bisectors is Incentre.

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Triangle ABC is similar to triangle PQR. The bisector of angle BAC meets BC at point D and the bisector of angle QPR meets QR at point M. Which of the following is correct?

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.

Q. is the point where all the perpendicular bisectors of the sides of a triangle meet.

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$(1)$ Orthocentre	(A) The point of intersection of the perpendicular bisectors of the sides of a triangle.
$(2)$ Centroid	(B) The point at which the three angle bisectors of a triangle meet.
$(3)$ Circumcentre	(C) The point at which the altitudes of a triangle meet.
$(4)$ Incentre	(D) The point at which the medians of a triangle meet.

The correct option is A 1C,2D,3A,4BPoint of intersection of all the altitudes is Orthocentre.Point of intersection of all the medians is Centroid.Point of intersection of all the perpendicular bisectors is Circumcentre.Point of intersection of all the angle bisectors is Incentre.

The correct option is A $1 C, 2 D, 3 A, 4 B$
Point of intersection of all the altitudes is Orthocentre.
Point of intersection of all the medians is Centroid.
Point of intersection of all the perpendicular bisectors is Circumcentre.
Point of intersection of all the angle bisectors is Incentre.