Median-Altitude

Median

In a triangle, a line joining the midpoint of a side to the opposite vertex is called a median.

AD is a median of ABC.

In any triangle, it can be proved that all the three medians meet at a point. The point where the three medians meet is called the Centroid of the triangle. The point G is the centroid in ABC in the following figure.

Altitude

In a triangle, the perpendicular from a vertex to the opposite side is called the Altitude.

In ABC of the following figure, AD is the altitude.

Three altitudes always meet at a point called Orthocentre of the triangle.

In Fig.(i): AD, BE, CF are the altitudes. O is the orthocentre. O lies inside the acute angled triangle.

In Fig.(ii): AB, CB and BD are the altitudes. B is the orthocentre.

In Fig.(iii): Three altitudes AD, BE, CF are produced to meet at O. O lies outside the obtuse angled triangle.

In a triangle, the bisectors of the three angles meet at a point called the Incentre.

In ABC in the figure above, the bisectors of the three angles meet at I. I is the Incentre.

With I as centre and IM as radius, a circle drawn to touch the sides, is called the Incircle.

In a triangle, the perpendicular bisectors of the three sides meet at a point called the Circumcentre.

In ABC, OD, OE, OF are the perpendicular bisectors of sides BC, AC and AB. O is called the circumcentre.

With O as centre and OA as radius a circle drawn will pass through B and C. Such a circle is called the Circumcircle.