BAIT #67 HGEO

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

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the three altitudes of a triangle intersect. It can be located inside, outside, or on the triangle depending on the type of triangle.

Front

What is 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.

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is the center of mass of the triangle and divides each median into a 2:1 ratio.

Front

If the length of median BF is 20, what is the length of segment FC?

Back

FC is also 20, since the median divides the opposite side into two equal segments.

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.

Front

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

Back

To find the circumcenter, calculate the perpendicular bisectors of at least two sides of the triangle and find their intersection point.

Front

What is the significance of the orthocenter in triangle geometry?

Back

The orthocenter helps in understanding the altitudes of a triangle and can be used in various geometric constructions and proofs.

Front

What is the formula for finding the length of a median in a triangle?

Back

Front

What is the difference between the circumcenter and the incenter?

Back

The circumcenter is equidistant from the vertices of the triangle, while the incenter is equidistant from the sides of the triangle.