Exam 8: Locus and Concurrence

How is the apothem of a regular polygon related to the side of the polygon to which it is drawn?

is an equilateral triangle with center O . If the distance from O to each vertex is 6 cm, how long is each side of ?

For the regular pentagon shown, find the measure of a central angle.

In , angle-bisectors , , and are concurrent at point X . If m = 27 ° and m = 32 ° , find m .

In a regular pentagon, each side has the length 4.8 inches while the apothem has the length 7.4 inches. To the nearest tenth of an inch, find the length of the radius of the pentagon.

To locate the circumcenter of a triangle, one must construct or draw all three perpendicular-bisectors of the sides of that triangle.

Determine the number of sides in a regular polygon whose central angles each measure 24°.

To construct an isosceles triangle with vertex angle and legs of length RS :

A circle can be inscribed within or circumscribed about any regular polygon.

For , what is the name of the circle that has its center O determined by the three perpendicular-bisectors of the sides of the triangle and radius of length OA ?

To construct the square ABCD with the diagonal as shown, begin by constructing the perpendicular-bisector of .

For equilateral triangle with center O , (if drawn)would be an apothem.

In a regular polygon with center O and a side , m = 72 ° . If AB = 4.6 inches, find the perimeter of the regular polygon.

If m = 90 ° in right triangle , then is an altitude of that triangle.

The three altitudes of an obtuse triangle are concurrent at a point that lies in the exterior of that triangle.

In , AB = BC = 17 and AC = 16. Find the distance from the centroid of to side .

How many different lines can be concurrent at point X?

The point at which the three angle-bisectors of the angles of a triangle are concurrent is known as the circumcenter of the triangle.

In , the medians are , , and . If RM = 9, SN = 12, and TP = 16, find the distance from the centroid of this triangle to the midpoint of side .

For what type of triangle are the angle-bisectors, perpendicular-bisectors of sides, altitudes, and medians the same?