Circumscribed Angles in Circles

Tangent Segments and Circumscribed Angles

Students will be able to solve problems involving tangent lines of circles and circumscribed angles with 80% class accuracy!

​Objective

GM: G-C.A.2 Identify and describe relationships among inscribed angles, radii, and chords, including the following: the relationship that exists between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; and a radius of a circle is perpendicular to the tangent where the radius intersects the circle

​Standard

Standard and Learning Objective

Multiple Choice

What is the diameter of a circle

• pi

• The longest chord (the chord must pass through the center)

• Any line segment inside a circle

• A straight line starting at the center and going to the circumference of a circle

Multiple Choice

What is the radius of a circle

• pi

• The longest chord (the chord must pass through the center)

• Any line segment inside a circle

• A straight line starting at the center and going to the circumference of a circle

Multiple Choice

What is the radius of this circle?

• 12

• 8

• 6

• 4

Multiple Choice

What is the diameter of this circle?

• 12

• 8

• 6

• 4

Multiple Choice

What is the measure of arc PQ?

• 85

• 170

• 42.5

• 8.5

Multiple Choice

What is the measure of angle PQR?

• 90

• 180

• 9

• 45

Point of tangency

tangent segment

Fill in the Blanks

A______________ is an angle formed by

two rays from a common endpoint that are tangent to a circle.

A circumscribed angle is an angle formed by

two rays from a common endpoint that are tangent to a circle.

Fill in the Blanks

2. In this diagram segment DB and segment DC are tangent to circle A at B and C respectively. What

is the measure of angle BDC?

Fill in the Blanks

3. If segment DB=6, then what is the measure of segment DC?

Let's Practice!