# 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 \(ABD\).

### Solution

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### 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 \(AB\).

### Solution

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### 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 \(P\)?

point \(A\)

point \(B\)

point \(C\)

point \(D\)

### Solution

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### Problem 4

The arc from \(A\) to \(B\) not passing through \(C\) measures 50 degrees. Select **all** the true statements.

Angle \(BCA\) measures 50 degrees.

Angle \(BCA\) measures 25 degrees.

Angle \(BOA\) measures 50 degrees.

The arc from \(B\) to \(C\) not passing through \(A\) measures 180 degrees.

Angles \(CBO\) and \(CAO\) are congruent.

### Solution

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(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

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(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

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(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?

3

\(\frac13\)

\(\text-\frac{1}3\)

-3

### Solution

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(From Unit 6, Lesson 12.)