# Isotomic and Isogonal Conjugates

- Author:
- Steve Phelps

## 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*PA*,*PB*, 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*PA*,*PB*, and*PC*about the angle bisectors of*A*,*B*, 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*PA*,*PB*, 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*PA*,*PB*, and*PC*about the angle bisectors of*A*,*B*, and*C*respectively. These three reflected lines concur at the isogonal conjugate of*P*.## New Resources

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