Warm UpDirections: Create your own definition for as many of

the vocabulary words listed below. You may use diagrams in your explanations.

circle radius diameter

radii chord secant

tangent concentric circles

common tangent point of tangency

Using a compass…Construct a circle, remember to label the

center of the circle before drawing your circle. Label the circle Q.

Then, using a straightedge, draw a line tangent to the circle. Label this line l.

Connect a radius from the center to the point of tangency. Label this point P.

What do you notice?

Theorem 10.1 If a line is tangent to a circle, then it is

perpendicular to the radius drawn to the point of tangency.

If l is tangent to ⨀Q at P, then l .

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PQ

Theorem 10.2In a plane, if a line is perpendicular to a

radius of a circle at its endpoint on the circle, then the line is tangent to the circle.

If l at P, then l is tangent to ⨀Q.

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PQ

Theorem 10.3If two segments from the same exterior

point are tangent to a circle, then they are congruent.

⨀

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If SR and ST are tangent to P, then SR ≅ ST.

Tell whether the line or segment is best described as a chord, a secant, a tangent, a diameter, or a radius of C.⨀

A diameter is a chord but not all chords are diameters

Common tangent: A line or segment that is tangent to two coplanar circles A common internal

tangent intersects the segment that joins the centers of the two circles.

A common external tangent does not intersect the segment that joins the centers of the two circles.

How many common tangents are there?

4 common tangents: 2 external and 2 internal

3 common tangents: 2 external and 1 internal

How many common tangents are there?

2 common tangents: 2 external and 0 internal

1 common tangents: 1 external and 0 internal

How many common tangents are there?

0 common tangent

0 common tangent

Segment AB is tangent to C at B. Segment AD ⨀is tangent to C at D. Find the value of x. ⨀

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x 2 − 4 = 21

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x 2 = 25

x = 25

x = ±5

You are standing at C, 14 feet from a water tower. The distance from you to a point of tangency on the tower is 28 feet. What is the radius of the water tower?

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r2 + 282 = (r +14)2

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r2 + 784 = r2 + 28r +196

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784 = 28r +196

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588 = 28r

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21 = r

Is segment CE tangent to D? ⨀Explain.

Find the values of x, y, and z in the diagram.