Central Angles Assignment

Chords DE, EF, and FG are congruent. Circle C is shown. Line segments C D, C E, C F, and C H are radii. Secants D E, E F, and F G are congruent. Angle H C D is 75 degrees, angle E C D is 67 degrees, and angle C F G is 56.5 degrees. Determine the following measures. mArc F G = ° m∠ECF = °

67 67

LK is tangent to circle J at point K. Circle J is shown. Line segment J K is a radius. Line segment K L is a tangent that intersects at point K. A line is drawn from point L through a point on the circle to the center point J. The length of the radius is r, the length of K L is 11, and the length of the line segment from point L to the point on the circle is 6. What is the length of the radius?

85/12

In ⊙H, Arc I K ≅ Arc J K, mArc I K = (11x + 2)°, and mArc J K = (12x - 7)°. Circle H is shown. Line segments H I, H K, and H J are radii. Lines are drawn to connect points I and K, and points K and J to form congruent secants. What is the measure of Arc I J K? mArc I J K = °

202

AB is tangent to ⊙C at point B and AD is tangent to ⊙C at point D. What is m∠A?

56

Circle P is shown. Line segment P Q is a radius and has a length of 9. Line Q R is a tangent that intersects the circle at point Q and has a length of 12. A line connects points R and P. The distance between point R and the circle is x, and the point on the circle to point P is a radius. What value of x would make Line R Q tangent to circle P at point Q? x =

6

In circle Q, ∠RQS ≅ ∠SQT. Which statement must be true?

RS ≅ ST

Line segment L N is tangent to circle O at point M and QM is a diameter. Circle O is shown. Line segment Q M is a diameter. Line segments P M and Q R are secants. Line segment N L is a tangent and intersects the circle at point M. Angle P M O is 27 degrees and angle M Q R is 42 degrees. Determine the measure of the following angles. The measure of ∠QML is degrees. The measure of ∠PMN is degrees.

90 63

The minor arc measures of circle Z are shown in the figure.Circle Z is shown. Radii Z Y, Z X, Z W, Z V, Z U, and Z T are shown. The arc measure of Y X is 71 degrees, the arc measure of X W is 32 degrees, the arc measure of W V is 71 degrees, the arc measure of V U is 78 degrees, the arc measure of U T is 54 degrees, and the arc measure of T Y is 54 degrees.Use the drop-down menus to complete each statement.

TZY YZX

Circle A is congruent to circle J. Chords BC, CF, EG, KL, LO, and MP are congruent. Which arcs are congruent? Check all that apply.

1,4,5

Circle J is congruent to circle P. If OK = 2x, QR = 12, and RT = x + 3, what is the length of chord KM?

9