In triangle ABC, if D is the circumcenter, what is true about point D?

Point D is equidistant from points A, B, and C.

What is the difference between the circumcenter and the incenter?

The circumcenter is the point where the perpendicular bisectors meet and is equidistant from the vertices, while the incenter is the point where the angle bisectors meet and is equidistant from the sides.

How can you determine if a point is the circumcenter?

A point is the circumcenter if it is equidistant from all three vertices of the triangle.

What is the formula to find the circumradius (R) of a triangle?

The circumradius R can be calculated using the formula R = (abc) / (4K), where a, b, and c are the lengths of the sides of the triangle and K is the area of the triangle.

What is the relationship between the circumradius and the sides of a triangle?

The circumradius is directly related to the lengths of the sides of the triangle and the area; larger sides generally lead to a larger circumradius.

If a triangle has a circumradius of 10, what does this imply?

This implies that the circumcircle of the triangle has a radius of 10 units, meaning all vertices are 10 units away from the circumcenter.

What is the role of the circumcenter in triangle similarity?

The circumcenter helps in establishing similarity between triangles by providing a common reference point for comparing distances to vertices.

How does the circumcenter change with different types of triangles?

In an acute triangle, the circumcenter is inside the triangle; in a right triangle, it is on the hypotenuse; and in an obtuse triangle, it is outside the triangle.

Circumcenter

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSG.C.A.3, HSG.CO.C.9

Standards-aligned

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15 questions

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FLASHCARD QUESTION

Front

What is 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.

Tags

CCSS.HSG.C.A.3

FLASHCARD QUESTION

Front

What does the Perpendicular Bisector Theorem state?

Back

The Perpendicular Bisector Theorem states that any point on the perpendicular bisector of a segment is equidistant from the endpoints of that segment.

Tags

CCSS.HSG.CO.C.9

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.

Tags

CCSS.HSG.C.A.3

FLASHCARD QUESTION

Front

What is the relationship between the circumcenter and the vertices of a triangle?

Back

The circumcenter is equidistant from all three vertices of the triangle.

Tags

CCSS.HSG.C.A.3

FLASHCARD QUESTION

Front

If D is the circumcenter, what can be said about segments DA, DB, and DC?

Back

Segments DA, DB, and DC are all equal in length, as they are all radii of the circumcircle.

Tags

CCSS.HSG.C.A.3

FLASHCARD QUESTION

Front

What is a circumcircle?

Back

A circumcircle is a circle that passes through all the vertices of a polygon, specifically a triangle in this context.

FLASHCARD QUESTION

Front

What is the significance of the circumcenter in triangle construction?

Back

The circumcenter is used to construct the circumcircle, which is essential in various geometric constructions and proofs.

Tags

CCSS.HSG.C.A.3

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