Circumcenter/Incenter
Flashcard
•
Mathematics
•
9th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the definition of the circumcenter of a triangle?
Back
The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is equidistant from all three vertices of the triangle.
2.
FLASHCARD QUESTION
Front
What is the definition of the incenter of a triangle?
Back
The incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all three sides of the triangle.
3.
FLASHCARD QUESTION
Front
How do you find the circumcenter of a triangle?
Back
To find the circumcenter, construct the perpendicular bisectors of at least two sides of the triangle. The point where they intersect is the circumcenter.
4.
FLASHCARD QUESTION
Front
How do you find the incenter of a triangle?
Back
To find the incenter, construct the angle bisectors of at least two angles of the triangle. The point where they intersect is the incenter.
5.
FLASHCARD QUESTION
Front
What is the relationship between the circumcenter and the circumradius?
Back
The circumradius is the radius of the circumcircle, which is the circle that passes through all three vertices of the triangle. The circumcenter is the center of this circle.
6.
FLASHCARD QUESTION
Front
What is the relationship between the incenter and the inradius?
Back
The inradius is the radius of the incircle, which is the circle that is tangent to all three sides of the triangle. The incenter is the center of this circle.
7.
FLASHCARD QUESTION
Front
If a triangle has vertices A, B, and C, how can you find the circumcenter using coordinates?
Back
To find the circumcenter using coordinates, calculate the midpoints of two sides, find the slopes of those sides, determine the slopes of the perpendicular bisectors, and solve the equations of the lines to find their intersection.
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