module 15: angles and segments in circles...module 15: angles and segments in circles a circle is...
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Module 15: Angles and Segments in Circles
A circle is the set of points in a plane at a given distance ( radius)from a given point (center).You name a circle by its center. The circle on the bicycle wheel withcenter O, is called circle O.Radius: segment from the center to a point on the edge of the circle.
Lessons 15.1 to 15.3
Part 1
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Congruent Circles: Circles with the same radius.
Concentric Circles: Coplanar circles with the same center.
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Circle Terms 15.1, page 779
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Point on Tangency:The point where the tangent touches the circle. Example: point B, and point C.
.R
S
. .Secant:Is a line that intersects the circle twice: 𝑹𝑺
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Central Angle: Angle whose vertex is at the center of the circle and the sides are radius of the circle.
15.1, page 779
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Inscribed Angle: Angle whose vertex is on the circle and the sides are chords.
15.1, page 779
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MAJOR ARC page 780
SEMICIRCLE Page 780
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15.1, page 781
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15.1, page 782
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Theorem:Inscribed Angles intercepting the same arc are congruent.
Since both inscribed ⦟ABC and ⦟ADC intercept the same 𝑨𝑪,then m ⦟ABC = m ⦟ADC
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15.1, page 785
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Cyclic (inscribed) Quadrilateral:A quadrilateral inscribed in a circle.All vertices are on the circle.
⦟D + ⦟B = 180° and ⦟A + ⦟C = 180°
15.2, page 794
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Page 782
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15.3, page 806
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15.3, page 808
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Solution
90°
90°
140°40°
OR 180° - 140° = 40°
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𝑨𝑵 ≅ 𝑮𝑵
Tangent Segments
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16 cm
7 cm4 cm
By the Tangent Theorem, m ⦟T = 90° and m ⦟ P = 90°.⦟T + ⦟P = 180°, therefore they are supplementary.Since ⦟T and ⦟P are consecutive interior and supplementary, then by the converse of the parallel lines theorem 𝑻𝑵 ǁ 𝑷𝑴,therefore NMPT is a trapezoid .Since NMPT is a trapezoid, then
Area = 𝒉 (𝒃𝟏+𝒃𝟐)
𝟐=
𝟏𝟔 (𝟕+𝟒)
𝟐= 88 𝒄𝒎𝟐
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Homework:Online Assignment15.1-15.2, & 15.3
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Quiz: Equations of Circles (20 minutes)
Multiple choice
Answer each question from 1-8
Choose one from 9 & 10
Show your work