Geo B Mod 4 Circle Theorems Lesson #1

Circle Theorems

Circle Theorem

The tangent to a circle is perpendicular to the radius at the point of contact.

Multiple Choice

Name a tangent.

• Segment XC
• Segment LM
• Segment HJ
• LINE BD

Multiple Choice

Segment ED is tangent to circle O. What is the value of x?

*Hint: All the angles in a triangle make 180 degrees, and because DE is a tangent line, the angle at D is 90 degrees!

• 232

• 52

• 79

• 115

Multiple Choice

Assume both lines are tangent to circle O. What is the value of x?

• 90

• 115

• 120

• 45

Circle Theorem

The angle at the circumference is double the angle at the centre.

Inscribed Angle

• An inscribed angle in a circle has a vertex on the circle and is formed by two chords.

• The measure of an inscribed angle is half the measure of its corresponding arc of the circle.

Fill in the Blanks

Multiple Choice

• $$m\angle PQR=68\degree$$

• $$m\angle PQR=34\degree$$

• $$m\angle PQR=292\degree$$

• $$m\angle PQR=112\degree$$

Circle Theorem

Two tangents from a point to a circle are equal.

Multiple Choice

How can we solve for x in this example?

• add both expressions together and subtract from 360

• set both expressions equal to each other

• use Pythagorean Theorem

• use magic

• combine like terms

Solve for x.

3x - 10 = 2x +5

x - 10 = 5

x = 15

Multiple Choice

A is a common external point and B and D are both points of tangency. What is the length of AB?

• 32.8

• 4

• 7.6

• 22

Fill in the Blanks

End of Lesson #1

When you have finished this lesson, take a screenshot of your results and upload it to the assignment page on Canvas. You have multiple attempts so be sure to go back and review the questions as many times as you need to get the grade you want. ​

Geo B Module 4 Lesson #1