Perpendicular Bisectors and the Circumcenter: Practice Level 1 | Geometry

Level 1 · Foundational 0 / 12 answered

Question 1 of 12

1

What defines the perpendicular bisector of a nonzero segment?

Answer choices for question 1 A Any line through an endpoint B The line perpendicular to the segment through its midpoint C Any line parallel to the segment D Any segment joining the endpoints
2

M is the midpoint of AB, and PM is perpendicular to AB. Which statement follows?

Answer choices for question 2 A $PA=PB$ B $PA=AB$ C $PM=AB$ D $PA=PM$
3

Q is equally far from distinct points A and B. Where must Q lie?

Answer choices for question 3 A At A B At B C On every line through A D On the perpendicular bisector of AB
4

A segment is 18 cm long. How far is its midpoint from each endpoint?

Answer choices for question 4 A 18 cm B 36 cm C 9 cm D 4.5 cm
5

P lies on the perpendicular bisector of AB. PA is 16 cm. What is PB?

Answer choices for question 5 A 16 cm B 8 cm C 32 cm D It cannot be found
6

Equal-radius circles centered at A and B are used to construct the perpendicular bisector of a 10 cm segment. Which radius gives two distinct crossings?

Answer choices for question 6 A 5 cm B 4 cm C 6 cm D 2 cm
7

What does a locus describe?

Answer choices for question 7 A One example of a point B All points that satisfy a specified condition C Only points inside a triangle D The length of a segment
8

Which triangle lines meet at the circumcenter?

Answer choices for question 8 A The three side lines B Three lines through the vertices parallel to opposite sides C The lines joining adjacent vertices D The perpendicular bisectors of the three sides
9

Which distances are guaranteed equal at a triangle circumcenter O?

Answer choices for question 9 A
$AB=BC$

$BC=CA$
B The distances from O to the three side lines C
$OA=OB$

$OB=OC$
D The lengths of the three side bisectors
10

Where is the circumcenter of a right triangle?

Answer choices for question 10 A At the right-angle vertex B At the midpoint of either leg C Always outside the triangle D At the midpoint of the hypotenuse
11

What is the circumcircle of a nondegenerate triangle?

Answer choices for question 11 A The circle passing through all three vertices B A circle through only two vertices with arbitrary center C A circle tangent to all three side lines D A circle with radius equal to every side length
12

For one given rotation, A maps to a different point A prime. Why does the center lie on the perpendicular bisector of their chord?

Answer choices for question 12 A The chord is always a diameter B The center is equally far from A and A prime C The chord always passes through the center D A and A prime are equally far from every point