Is the orthocenter and incenter of a triangle the same point?

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Although the orthoceneter and the incenter of a triangle are technically different things:

The point in which the three altitudes of a triangle meet is called the orthocenter of the triangle.

The point in which the three bisectors of the angles of a triangle meet is called the incenter of the triangle.

. . . Are they the same point?

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2 Answers

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No, they are not (though they can be). The incenter is, by construction, always inside the triangle, while the orthocenter can possibly be outside the triangle. (Consider a very obtuse triangle)

You can play with the orthocenter visually here, and the incenter here

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They will coincide precisely when each bisector is an altitude--that is, for equilateral triangles.

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