Circle Theorems

ARC MEASURES

100

Find the measure of arc BC

140 degrees

200

Find the measure of arc DF

129 degrees

300

Find arc CFD 

306 degrees

400

DOUBLE POINT QUESTION! 

Find the measure of arc AD

48 degrees

500

Find angle SPQ 

146 degrees

ANGLES

100

Find angle CDE. 

76 degrees

200

DOUBLE POINT QUESTION! Given that angle ABC is 27 degrees, find the measure of angle BAD

153 degrees

300

Find the sum of the measures ACB and DAE

75 degrees

400

Find the missing angles n, p, m

n = 41 degrees

p = 61 degrees

m = 29 degrees

500

DOUBLE POINT QUESTION! Find angles x, y, z

x = 40 degrees

y = 25 degrees

z = 115 degrees

TANGENT AND SECANTS

100

Find the measure of angle V

114 degrees

200

DOUBLE POINT QUESTION! Find the measure of the arc AD and CB

AD = 80 degrees

CB = 30 degrees

300

Find x

x = 40 degrees

400

Find the measure of angle DFE and DGB

angle DFE = 67 degrees

angle DGB = 88 degrees

500

DOUBLE POINT QUESTION! The radius of circle 𝑨 is 𝟒. 𝑫𝑪̅ and 𝑪𝑬̅ are tangent to the circle with 𝑫𝑪 = 𝟏𝟐. Find the measure of angle C, the arc 𝑫𝑬, and the area of quadrilateral 𝑫𝑨𝑬𝑪 rounded to the nearest hundredth.

Angle C = 36.87 degrees

Measure DE = 143.13 degrees

The area of DAEC = 48 square units

SURPRISE ME

100

True or False: 

Opposite angles of an inscribed quadrilateral must be congruent. 

False

200

DOUBLE POINT QUESTION! 

Always, sometimes, never: 

When a line bisects a chord, that line ______ passes through the center of the circle. 

Sometimes

300

Always, Sometimes, Never: 

An angle inscribed in a semicircle is ______ a right angles. 

Always

400

True or False? A diameter that is perpendicular to a chord must bisect the chord. 

True

500

Always, sometimes, never: 

If a line is tangent to a circle, then the line is perpendicular to the radius drawn at the point of tangency. 

Always