POC problems

Front

What is the definition of an incenter in a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect. It is also the center of the circle inscribed within the triangle.

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 the center of the circumcircle, which passes through all three vertices of the triangle.

Front

If the measure of angle CAP is 34°, what is the measure of angle CAB if the triangle is isosceles?

Back

68°

Front

In triangle ABE, if point D is the incenter, what can be said about angle ABD?

Back

Angle ABD is half the measure of the angle opposite to it in triangle ABE.

Front

What is the relationship between the lengths of segments in a triangle?

Back

The lengths of the segments in a triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.

Front

If AG = 10, what is the length of BG if G is the midpoint of segment AB?

Back

10

Front

What is the formula for finding the length of a segment in a triangle given the coordinates of its endpoints?

Back

Front

If PX = 5, what is the length of PZ if PZ is equal to PX?

Back

5

Front

What is the significance of the circumradius in a triangle?

Back

The circumradius is the radius of the circumcircle and is the distance from the circumcenter to any vertex of the triangle.

Front

How do you find the measure of an angle in a triangle when given the measures of the other two angles?

Back