10-5 Tangents You used the Pythagorean Theorem to find side lengths of right triangles. Use properties of tangents. Solve problems involving circumscribed.

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Presentation transcript:

10-5 Tangents You used the Pythagorean Theorem to find side lengths of right triangles. Use properties of tangents. Solve problems involving circumscribed polygons.

The line intersects the circle at one point. The line is called a tangent line. The point where it touches the circle is called the Point of tangency.

Common Tangents A common tangent is a line, ray or segment that is tangent to two circles in the same plane. l l F G F G

A. Copy the figure and draw the common tangents. If no common tangent exists, state no common tangent. Answer: These circles have no common tangents. Any tangent of the inner circle will intercept the outer circle in two points.

B. Copy the figure and draw the common tangents. If no common tangent exists, state no common tangent. Answer: These circles have 2 common tangents.

A.2 common tangents B.4 common tangents C.6 common tangents D.no common tangents A. Copy the figure and draw the common tangents to determine how many there are. If no common tangent exists, choose no common tangent.

A.2 common tangents B.3 common tangents C.4 common tangents D.no common tangents B. Copy the figure and draw the common tangents to determine how many there are. If no common tangent exists, choose no common tangent.

p. 733 What is the shortest distance from a tangent to the center of a circle? The radius drawn to the point of tangency

Find AC. A B C 33 cm 24 cm = c 2 c ≈ 40.80

Test to see if ΔKLM is a right triangle. ? = 29 2 Pythagorean Theorem 841 =841 Simplify. Answer:

A. B. What theorem can you use to answer this question (without guessing)? Theorem Radius must be perpendicular to the tangent.

Off on a tangent Draw a circle Add two tangent lines Extend the lines until they intersect. Measure the lengths of the two tangent segments from the circle to the intersection. What do you find about the distance from the point of tangency to the point of intersection?

p. 734

AC =BCTangents from the same exterior point are congruent. 3x + 2 =4x – 3Substitution 2 =x – 3Subtract 3x from each side. 5 =xAdd 3 to each side. Answer: x = 5

A.5 B.6 C.7 D.8

Circumscribed polygons The pentagon is circumscribed around the circle. All of its vertices touch the circle. The triangle is circumscribed around the circle. Each side touches the circle at exactly one point. A polygon is circumscribed about a circle if every side of the polygon is tangent to the circle.

Polygons Not Circumscribed

Step 1Find the missing measures.

Step 2Find the perimeter of ΔQRS. Answer: So, the perimeter of ΔQRS is 36 cm. = or 36 cm

10-5 Assignment Page 736, even, 20-22, 24-25