Post on 31-Dec-2015
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5-Minute Check on Lesson 10-45-Minute Check on Lesson 10-45-Minute Check on Lesson 10-45-Minute Check on Lesson 10-4 Transparency 10-5
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Refer to the figure and find each measure.
1. m1
2. m2
3. m3
4. m4
5. In ⊙B, find x if mA = 3x + 9and mB = 8x – 4.
6. If an inscribed angle has a measure of 110, what is the measure of its intercepted arc?Standardized Test Practice:
A CB D55 70 110 220
20°
60°
20°
100°
x = 11
D
Lesson 10-5
Tangents
Objectives
• Use properties of tangents
• Solve problems involving circumscribed polygons
Vocabulary
• Tangent – a line that intersects a circle in exactly one point
• Point of tangency – point where a tangent intersects a circle
ALGEBRA is tangent to at point R. Find y.
Because the radius is perpendicular to the tangent at the point of tangency, . This makes a right angle and a right triangle. Use the Pythagorean Theorem to find QR, which is one-half the length y.
Pythagorean Theorem
Simplify.
Subtract 256 from each side.
Take the square root of each side.
Because y is the length of the diameter, ignore the negative result.
Answer: Thus, y is twice .
Answer: 15
is a tangent to at point D. Find a.
First determine whether ABC is a right triangle by using the converse of the Pythagorean Theorem.
Determine whether is tangent to
Pythagorean Theorem
Because the converse of the Pythagorean Theorem did not prove true in this case, ABC is not a right triangle.
Answer: So, is not tangent to .
First determine whether EWD is a right triangle by using the converse of the Pythagorean Theorem.
Determine whether is tangent to
Pythagorean Theorem
Simplify.
Answer: Thus, making a tangent to
Because the converse of the Pythagorean Theorem is true, EWD is a right triangle and EWD is a right angle.
Answer: no
Determine whether is tangent to
ALGEBRA Find x. Assume that segments that appear tangent to circles are tangent.
are drawn from the same exterior point and are tangent to so are drawn from the same exterior point and are tangent to
Definition of congruent segments
Substitution.
Use the value of y to find x.
Definition of congruent segments
Substitution
Simplify.
Subtract 14 from each side.
Answer: 1
Triangle HJK is circumscribed about Find the perimeter of HJK if
Use Theorem 10.10 to determine the equal measures.
We are given that
Answer: The perimeter of HJK is 158 units.
Definition of perimeter
Substitution
Triangle NOT is circumscribed about Find the perimeter of NOT if
Answer: 172 units
Summary & Homework
• Summary:– A line that is tangent to a circle intersects the
circle in exactly one point.– A tangent is perpendicular to a radius of a circle– Two segments tangent to a circle form the same
exterior point are congruent
• Homework: – pg 556-558; 8-11, 12-17