Question

which is the only center point that lies on the edge of a triangle?

the incenter of a right triangle
the incenter of an obtuse triangle
the circumcenter of a right triangle
the circumcenter of an obtuse triangle

Explanation:

Analyze the location of the incenter

$$ \text{The incenter is the intersection of the angle bisectors and always lies strictly inside any triangle.} $$

Analyze the location of the circumcenter

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Determine the correct option

$$ \text{The circumcenter of a right triangle is the only center point listed that lies on the edge of a triangle.} $$

Answer:

• the incenter of a right triangle
• the incenter of an obtuse triangle
• the circumcenter of a right triangle (Correct answer)
• the circumcenter of an obtuse triangle