Deck 8: Locus and Concurrence

Question 1

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

Answer 1

NOT ANSWERED.

Question 2

How many different lines can be concurrent at point X?

Answer 2

NOT ANSWERED.

Question 3

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

Answer 3

True

Question 4

A number of lines are concurrent if they have exactly one point in common.

Question 5

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

Question 6

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 .

A)4
B)6
C)8
D)10

Question 7

In , m = 90 ° . If AC = 6 and BC = 8, find the distance from vertex C to the midpoint of hypotenuse .

A)3
B)4
C)5
D)5.6

Question 8

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

Question 9

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

Question 10

In , , , and are medians. If the centroid of the triangle is point C , find the relationship between TC and PC .

Question 11

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

A)angle-bisectors of a rectangle
B)perpendicular-bisectors of the sides of a rhombus
C)angle-bisectors of a trapezoid
D)angle-bisectors of a kite

Question 12

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

Question 13

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

Question 14

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

A)construct another angle congruent to
B)mark off an arc from B of length RS on side
C)mark off an arc from B of length RS to intersect both sides and
D)None of These

Question 15

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

Question 16

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

Question 17

If lines l, m, and n are concurrent, then:

A)they intersect at one point
B)they are parallel
C)they do not determine a plane
D)None of These

Question 18

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

Question 19

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

Question 20

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

Question 21

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

A)30 °
B)45 °
C)60 °
D)None of These

Question 22

In regular hexagon ABCDEF , AB = 12. Find the length of diagonal .

Question 23

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

Question 24

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

Question 25

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 ?

Question 26

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

Question 27

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

A)10
B)12
C)14
D)15

Question 28

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

A)36 °
B)72 °
C)108 °
D)None of These

Question 29

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.

A)2
B)2.5
C)3
D)4

Question 30

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

Question 31

Consider the triangle with sides of lengths a, b, and c. How would you construct a larger triangle similar to the first triangle but with a constant of proportionality of 2?

Question 32

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

Question 33

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

A)3 cm
B) cm
C)6 cm
D) cm

Question 34

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

A)9
B)12
C)15
D)18

Question 35

In regular decagon QRSTUVWXYZ , is a radius. Find m .

A)45 °
B)60 °
C)72 °
D)144 °

Question 36

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?

Question 37

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

Question 38

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?

Question 39

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

A)6
B)
C)
D)None of THese

Question 40

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

Question 41

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

Question 42

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

Question 43

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

Question 44

In an equilateral triangle whose radius has length 6, find the length of an apothem.

Question 45

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

Question 46

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

Question 47

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

Question 48

For a square ABCD , the length of radius is cm. Find the perimeter of ABCD .

Question 49

How is the radius of a regular polygon related to the angle to whose vertex the radius was drawn?

Question 50

To inscribe a circle in a square, the center can be found by the intersection of the two diagonals.

Question 51

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.