Incenter of a Triangle Worksheet
Explore the incenter of a triangle, its properties, and how to construct it with this Grade 9 geometry worksheet.
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Incenter of a Triangle
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Read each question carefully and answer to the best of your ability. Show all your work for construction problems.
1. The incenter of a triangle is the intersection point of the three .
2. The incenter is equidistant from the of the triangle.
3. The circle inscribed within a triangle, tangent to all three sides, is called the .
4. Every triangle has exactly one .
1. Which of the following statements about the incenter is true?
It is equidistant from the vertices.
It is the center of the circumscribed circle.
It is the intersection of the angle bisectors.
It is always outside the triangle.
2. If the incenter of a triangle is I, and the distance from I to side AB is 5 cm, what is the distance from I to side BC?
Less than 5 cm
Greater than 5 cm
Exactly 5 cm
Cannot be determined
1. Draw an obtuse triangle ABC. Construct all three angle bisectors to locate the incenter. Label the incenter 'I'.
2. In a triangle PQR, if angle P = 60° and angle Q = 80°, what is the measure of angle PIR, where I is the incenter?
1. The incenter of an equilateral triangle is also its centroid, orthocenter, and circumcenter.
True
False
2. The incenter of a right-angled triangle lies on its hypotenuse.
True
False
1. A triangular park needs a circular fountain installed such that it is equally distant from all three pathways forming the sides of the park. Where should the center of this fountain be located?
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