Lesson 3

Tangent Lines

Problem 1

Line $$BD$$ is tangent to a circle with diameter $$AB$$. Explain why the measure of angle $$BCA$$ must equal the measure of angle $$ABD$$.

Problem 2

Line $$AC$$ is perpendicular to the circle centered at $$O$$ with radius 1 unit. The length of $$AC$$ is 1.5 units. Find the length of segment $$AB$$.

Problem 3

Technology required. Line $$PD$$ is tangent to a circle of radius 1 inch centered at $$O$$. The length of $$PD$$ is 1.2 inches. The length of $$AB$$ is 1.7 inches. Which point on the circle is closest to point $$P$$?

A:

point $$A$$

B:

point $$B$$

C:

point $$C$$

D:

point $$D$$

Problem 4

The arc from $$A$$ to $$B$$ not passing through $$C$$ measures 50 degrees. Select all the true statements.

A:

Angle $$BCA$$ measures 50 degrees.

B:

Angle $$BCA$$ measures 25 degrees.

C:

Angle $$BOA$$ measures 50 degrees.

D:

The arc from $$B$$ to $$C$$ not passing through $$A$$ measures 180 degrees.

E:

Angles $$CBO$$ and $$CAO$$ are congruent.

Solution

(From Unit 7, Lesson 2.)

Problem 5

Chords $$AC$$ and $$DB$$ intersect at point $$E$$. List 3 pairs of angles that must be congruent.

Solution

(From Unit 7, Lesson 2.)

Problem 6

The image shows a circle with diameters $$AC$$ and $$BD$$. Prove that chords $$BC$$ and $$AD$$ (not drawn) are congruent.

Solution

(From Unit 7, Lesson 1.)

Problem 7

The line represented by $$y+3=\text-3(x+6)$$ is transformed by the rule $$(x,y)\rightarrow (\text-x,\text-y)$$. What is the slope of the image?

A:

3

B:

$$\frac13$$

C:

$$\text-\frac{1}3$$

D:

-3