Exam 8: Locus and Concurrence

For what type of regular polygon does the apothem have a length equal to one-half the length of a side of the polygon?

For a regular pentagon, the measure of each central angle is 72°.

In regular hexagon ABCDEF , diagonals and are drawn. Find m .

In regular octagon ABCDEFGH, AB = 6. Find the perimeter of trapezoid ABCH.

For , , , and are medians. If TP = 23.4 cm, find the distance between the centroid of and vertex T .

For , points A , B , C , D , and E are equally spaced on the circle in that order. If tangents are constructed at these points, what type of polygon circumscribes this circle?

In a regular polygon, each central angle measures 15°. How many sides does the polygon have?

Where M , N , and P are the midpoints of the sides of and C is the centroid of the triangle, it follows that .

If the length of each apothem of a square is a, then the length of each side is 2a.

Write the formula for the measure c of the central angle of a regular polygon of n sides.

In isosceles triangle , XY = YZ = 10, and XZ = 16. Where C is the centroid of , find the distance from C to side of the triangle.

To circumscribe a circle about regular hexagon ABCDEF , the center can be determined by the intersection of diagonals and .

For an equilateral triangle, the incenter and circumcenter are the same point.

To construct the altitude from vertex A to side of the obtuse triangle , one begins by constructing the midpoint of .

In order to circumscribe a circle about regular hexagon ABCDEF, we bisect angle A and B to determine center O as the intersection. What is the radius length for the circle?

Find the length of a side for a regular hexagon whose apothem has length cm.

In regular hexagon ABCDEF , is the apothem to side . If CD = 12, find OM

Which of the following lines (line segments)are concurrent?

For any regular polygon, the center can be determined by the intersection of any two angle-bisectors of the polygon.

Find the number of sides for a regular polygon in which each interior angle is 120° larger than each exterior angle.