Isogonal and Isotomic Conjugates

Consider a triangle

ABC

and a point

M

. The three line segments

AM

,

BM

and

CM

(red, then green) extended to meet the opposite sides are known as the cevians of the triangle with respect to

M

.

The angle bisectors of

ABC

are shown by red dashed lines.

The medians of

ABC

are shown by green dashed lines.

The reflections of the cevians (red lines) about the angle bisectors intersect at a point called the isogonal conjugate.

The reflections of the cevians (green lines) about the medians intersect at a point called the isotomic conjugate.

You can drag the points

A

,

B

,

C

and

M

.

Minh Trinh Xuan