Prove that the bisectors of the angles of any triangle ABC are concurrent. The point of intersection is called the incentre, I.(adsbygoogle = window.adsbygoogle || []).push({});

Proof:

-Angle A and B are bisected and their bisectors meet at a point I

-Assume a line segment bisects angle C and meets the bisector of angle A at point O

-Assume a line from O to B that will bisect angle B

-But angle B is already bisected by segment BI

-So line segment OB must be BI

-Thus point O is I

-Therefore the incentre is at I

Does this proof workout?

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# Converse Proof

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