Secants and Tangents

10.4

Learning Target & Do Now

LT: By the end of today I will know what secants and tangents are.

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DN: If a circle has an area of 64π² units, what is its circumference?

What is the eighth term in the following sequence?

4, 20, 100, 500...

16π units, 4*5⁷

Secants

• What was a chord again?
• A secant is the next step beyond a chord
• A secant is a line (not a segment!) that touches a circle at 2 points
• Every secant contains a chord

Tangents

• A tangent is a line that intercepts a circle at exactly one point.
• This is the point of tangency or point of contact
• Like chords, the distance is measured with the 丄 line from the center
• What length is this line?

A tangent line is 丄 to the radius drawn to the point of contact.

If a line is 丄 to a radius at its outer endpoint, then it is tangent to the circle.

Secant and Tangent Segments

• A tangent segment is a segment between the point of contact and a point outside the circle
• A secant segment is the segment joining a point�outside the circle to the farther intersection of the �circle
• The external part of the secant is the portion that connects the outside point to the nearer intersection with the circle

Example (Not the end of the slides though*)

*Mr Redmond has accidentally skipped the rest of this lesson at least twice.

The Two-Tangent Theorem

85. If two tangent segments are drawn to a circle from an external point, the tangent segments are congruent.

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Explain how this can be proven.

Tangent Circles

• Two circles are internally tangent if one is inside the other and they contact at one point. How do I draw the diagram?
• What about two externally tangent circles?

More Tangents

• PQ is the line of centers
• XY is the common internal tangent
• Tangent and crosses the line of centers
• AB is the common external tangent

Tangent Problem Procedures

1. Draw the segment joining the centers.
2. Draw the radii to the point of contact.
3. Draw a line parallel to the common tangent through the center of the smaller circle.
1. This line will intersect the radius of the larger circle to make a rectangle and a right triangle
4. Solve using knowledge of rectangles and triangles.

You Do