# Isotomic and Isogonal Conjugates

## Isotomic (Left) Conjugates and Isogonal (Right) Conjugates

The isotomic conjugate of a point P with respect to a triangle ABC is constructed by taking the lines PAPB, and PC. These lines intersect side BC, AC, and AB in points A', B', and C'. These points are reflected about the midpoints of their respective sides, resulting in points A'', B'', and C''. Lines AA'', BB'', and CC'' concur at the isotomic congugate of P. The isogonal conjugate of a point P with respect to triangle ABC is constructed by reflecting the lines PAPB, and PC about the angle bisectors of AB, and C respectively. These three reflected lines concur at the isogonal conjugate of P.

## Isotomic (Left) Conjugates and Isogonal (Right) Conjugates

The isotomic conjugate of a point P with respect to a triangle ABC is constructed by taking the lines PAPB, and PC. These lines intersect side BC, AC, and AB in points A', B', and C'. These points are reflected about the midpoints of their respective sides, resulting in points A'', B'', and C''. Lines AA'', BB'', and CC'' concur at the isotomic congugate of P. The isogonal conjugate of a point P with respect to triangle ABC is constructed by reflecting the lines PAPB, and PC about the angle bisectors of AB, and C respectively. These three reflected lines concur at the isogonal conjugate of P.