Honors Geometry Circles

In the diagram, central angle AOC measures 80 degrees. What is the number of degrees in the measure of inscribed angle ABC?

• 80

• 20

• 160

• 40

• 130

• 25

• 230

• 65

In the diagram with parallel chords, find the measure of the arc marked with an x.

• 40

• 80

• 120

• 240

• 15

• 25

• 60

• 30

In the diagram of circle O, PA is tangent to circle O at A, and PBC is a secant with points B and C on the circle.

If PA = 8 and PB = 4, what is the length of PC?

• 16

• 20

• 15

• 12

Secants JKL and JMN are drawn to circle O from an external point, J. If JK = 8, LK = 4, and JM = 6, what is the length of JN?

(Diagram not drawn to scale.)

• 16

• 12

• 10

• 8

• 87

• 61

• 43.5

• 26

In the diagram of circle O, chord AB is parallel to chord CD.

A correct justification for m arcAC = m arcBD in circle O is

• parallel chords intercept congruent arcs

• congruent chords intercept congruent arcs

• if two chords are parallel, then they are congruent

• if two chords are equidistant from the center, then the arcs they intercept are congruent

The angle formed by the radius of a circle and a tangent to that circle has a measure of

In the diagram, AC and AD are tangent to circle B at points C and D, respectively, and BC, BD, and BA are drawn.

If AC = 12 and AB = 15, what is the length of BD?

• 5.5

• 9

• 12

• 18