## Triangle Incentre-Circumcentre Collinearity

1) If *I* is the incentre of triangle *ABC*, then the circumcentre of triangle *BIC*, say *O*, lies on the angle bisector of angle *A*.

2) If *O* is the circumcentre of triangle *DEF*, then the circumcentre of triangle *EOF*, say *I*, lies on the perpendicular bisector of *EF*.

Triangle Incentre-Circumcentre Collinearity

Can you explain why (prove) the two results are true? If stuck, proofs of the two result are respectively given on p. 156-157 and p.176 of **Some Adventures in Euclidean Geometry**, which is available for purchase as downloadable PDF or printed book at *More Info*

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Michael de Villiers, 7 April 2010.