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Over Lesson 10–4 A.A B.B C.C D.D 5-Minute Check 1 60 Refer to the figure. Find m 1.

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Over Lesson 10–4 A.A B.B C.C D.D 5-Minute Check 2 20 Refer to the figure. Find m 2.

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Over Lesson 10–4 A.A B.B C.C D.D 5-Minute Check 4 100 Refer to the figure. Find m 4.

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Over Lesson 10–4 A.A B.B C.C D.D 5-Minute Check 5 11 find x if m A = 3x + 9 and m B = 8x – 4.

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Then/Now Use properties of tangents. Solve problems involving circumscribed polygons. In this lesson we will:

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Vocabulary tangent point of tangency common tangent

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Example 1 Identify Common Tangents 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.

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Example 1 Identify Common Tangents 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.

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A.A B.B C.C D.D Example 1 4 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.

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A.A B.B C.C D.D Example 1 3 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.

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Concept

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Example 2 Identify a Tangent Test to see if ΔKLM is a right triangle. ? 20 2 + 21 2 = 29 2 Pythagorean Theorem 841 =841 Simplify. Answer:

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A.A B.B Example 2 A. B.

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Example 3 Use a Tangent to Find Missing Values EW 2 + DW 2 =DE 2 Pythagorean Theorem 24 2 + x 2 =(x + 16) 2 EW = 24, DW = x, and DE = x + 16 576 + x 2 =x 2 + 32x + 256Multiply. 320 =32xSimplify. 10 =xDivide each side by 32. Answer: x = 10

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A.A B.B C.C D.D Example 3 12

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Concept

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Example 4 Use Congruent Tangents to Find Measures 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

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A.A B.B C.C D.D Example 4 7

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Example 5 Find Measures in Circumscribed Polygons Step 1Find the missing measures.

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Example 5 Find Measures in Circumscribed Polygons Step 2Find the perimeter of ΔQRS. Answer: So, the perimeter of ΔQRS is 36 cm. = 10 + 2 + 8 + 6 + 10 or 36 cm

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A.A B.B C.C D.D Example 5 56 cm

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Tangent Applications in Circles More Problems Using Pythagorean Theorem.

Tangent Applications in Circles More Problems Using Pythagorean Theorem.

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