Question

8 multiple choice 1 point 44. which of the following statements is false? the incenter of a triangle is equidistant from the sides of the triangle the circumcenter of a right triangle is on the triangle the incenter of an obtuse triangle is outside the triangle the circumcenter of a triangle is equidistant from the vertices of the triangle

Explanation:

Step1: Recall incenter properties

The incenter is the intersection of angle bisectors, equidistant from sides (always inside the triangle, regardless of triangle type).

Step2: Recall circumcenter properties

• Circumcenter of right triangle: midpoint of hypotenuse (on the triangle).
• Circumcenter is equidistant from vertices (definition, as it's the center of the circumscribed circle).
• Incenter of obtuse triangle: still inside the triangle (since angle bisectors of an obtuse triangle meet inside). So the statement "The incenter of an obtuse triangle is outside the triangle" is false.

Answer:

The option: "The incenter of an obtuse triangle is outside the triangle" (the third option among the given choices)