Circumcenters of Triangles Practice

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.

Front

True or False: A circle that hits all the vertices of a polygon is circumscribed about the polygon.

Back

True

Front

True or False: The circumcenter is equidistant to the vertices of the triangle.

Back

True

Front

If KL=48 and LI=55, what is HK? (use the Pythagorean Theorem)

Back

73

Front

If KM=16 and HJ=126, what is KJ? (use the Pythagorean Theorem)

Back

65

Front

If IK=25, KN=7, KM=8, what is HK?

Back

25

Front

What is the formula for the Pythagorean Theorem?

Back

a² + b² = c², where c is the hypotenuse.

Front

What does it mean for a triangle to be circumscribed?

Back

A triangle is circumscribed when a circle can be drawn around it that touches all three vertices.

Front

How do you find the circumcenter of a triangle using its vertices?

Back

To find the circumcenter, calculate the midpoints of at least two sides, then find the slopes of those sides, determine the slopes of the perpendicular bisectors, and solve the equations to find their intersection.

Front

What is the relationship between the circumradius and the circumcenter?

Back

The circumradius is the radius of the circumcircle, which is centered at the circumcenter and passes through all three vertices of the triangle.