Over Lesson 10–6 A.A B.B C.C D.D 5-Minute Check 1 70 Find x. Assume that any segment that appears...
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Over Lesson 10–6 A. A B. B C. C D. D 70 Find x. Assume that any segment that appears to be tangent is tangent.
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Transcript of Over Lesson 10–6 A.A B.B C.C D.D 5-Minute Check 1 70 Find x. Assume that any segment that appears...
Over Lesson 10–6
A. A
B. B
C. C
D. D
70
Find x. Assume that any segment that appears to be tangent is tangent.
Over Lesson 10–6
A. A
B. B
C. C
D. D
125
Find x. Assume that any segment that appears to be tangent is tangent.
Over Lesson 10–6
A. A
B. B
C. C
D. D
110
Find x. Assume that any segment that appears to be tangent is tangent.
Over Lesson 10–6
A. A
B. B
C. C
D. D
35
Find x. Assume that any segment that appears to be tangent is tangent.
Over Lesson 10–6
A. A
B. B
C. C
D. D
125
What is the measure of XYZ if is tangent to the circle?
• Find measures of segments that intersect in the interior of a circle.
• Find measures of segments that intersect in the exterior of a circle.
Use the Intersection of Two Chords
A. Find x.
AE • EC = BE • ED Theorem 10.15
x • 8 = 9 • 12 Substitution
8x = 108 Multiply.
x = 13.5 Divide each side by 8.
Answer: x = 13.5
Use the Intersection of Two Chords
B. Find x.
PT • TR = QT • TS Theorem 10.15
x • (x + 10) = (x + 2) • (x + 4) Substitution
x2 + 10x = x2 + 6x + 8 Multiply.
10x = 6x + 8 Subtract x2 from each side.
Use the Intersection of Two Chords
4x = 8 Subtract 6x from each side.
x = 2 Divide each side by 4.
Answer: x = 2
Find Measures of Segments in Circles
BIOLOGY Biologists often examine organisms under microscopes. The circle represents the field of view under the microscope with a diameter of 2 mm. Determine the length of the organism if it is located 0.25 mm from the bottom of the field of view. Round to the nearest hundredth.
Find Measures of Segments in Circles
Understand Two cords of a circle are shown. Youknow that the diameter is 2 mm and thatthe organism is 0.25 mm from thebottom.
Plan Draw a model using a circle. Let xrepresent the unknown measure of theequal lengths of the chordwhich is the length of the organism. Use the products of the lengths of the intersecting chords to findthe length of the organism.
Find Measures of Segments in Circles
Solve The measure of ED = 2.00 – 0.25 or1.75 mm.
HB ● BF = EB ● BG Segment products
x ● x = 1.75 ● 0.25 Substitution
x2 = 0.4375 Simplify.
x ≈ 0.66 Take the square root ofeach side.
Answer: The length of the organism is 0.66millimeters.
Find Measures of Segments in Circles
Check Use the Pythagorean Theorem to checkthe triangle in the circle formed by theradius, the chord, and part of thediameter.
1 ≈ 1
12 ≈ (0.75)2 + (0.66)2?
1 ≈ 0.56 + 0.44?
A. A
B. B
C. C
D. D
10 ft
ARCHITECTURE Phil is installing a new window in an addition for a client’s home. The window is a rectangle with an arched top called an eyebrow. The diagram below shows the dimensions of the window. What is the radius of the circle containing the arc if the eyebrow portion of the window is not a semicircle?
Use the Intersection of Two Secants
Answer: 34.5
Theorem 10.16
Substitution
Distributive Property
Subtract 64 from each side.
Divide each side by 8.
Use the Intersection of a Secant and a Tangent
Answer: Since lengths cannot be negative, the value of x is 8.
LM is tangent to the circle. Find x. Round to the nearest tenth.
LM2 = LK ● LJ
122 = x(x + x + 2)
144 = 2x2 + 2x
72 = x2 + x
0 = x2 + x – 72
0 = (x – 8)(x + 9)
x = 8 or x = –9
A. A
B. B
C. C
D. D
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Find x. Assume that segments that appear to be tangent are tangent.
