Question

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 two triangles meet.

A) \[1c,2d,3a,4b\]
B) \[1a,2b,3c,4d\]
C) \[1b,2c,3d,4a\]
D) \[1d,2a,3b,4c\]

Answer 1

Hint: In order to answer this question, we have to understand the meanings of the given terms i.e. orthocentre, centroid, circumcentre and incentre. For this we have to know the meanings of terms involved such as median, angle bisectors, altitudes etc.

Complete step-by-step answer:
Given to us are four terms. Let us understand their meanings individually.
A triangle consists of three sides and the three points where these sides meet are known as vertex. For example, in a triangle ABC, the sides are AB, BC and CA and the vertex are A, B, C.
 $ 1) $ Orthocentre: Orthocentre is a point where the three altitudes of a triangle meet. Here, altitude is a line that passes through one vertex of the triangle and is perpendicular to the opposite side.
 $ 2) $ Centroid: Centroid is a point where the medians of the triangle meet.
 $ 3) $ Circumcentre: The point at which the perpendicular bisectors of the sides of a triangle.
 $ 4) $ Incentre: The point at which the angle bisectors meet is known as incentre.
So, the correct answer is “Option A”.

Note: A median of a triangle is the line joining one vertex of that triangle to the midpoint of its opposite side. Angle bisector of a triangle is the line that cuts the angle of a vertex of the triangle into two equal parts.