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Published byEsmond Elvin Ball Modified over 9 years ago
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Warm – up Session 48
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EOCT Review
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Homework Review
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CCGPS Geometry UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MMC9-12.G.C.1-5,G.GMD.1-3 Today’s Question: What other angle relationships do we know for circles? Standard: MMC9-12.G.C.2
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TANGENT: a LINE that intersects the circle exactly ONE time
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Point of Tangency
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Two circles can intersect… in two points one point or no points
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No points of intersection (different center)
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No points of intersection (same center) Same center but different radii
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1 point of intersection (Tangent Circles) Internally Tangent Externally Tangent
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2 points of intersection
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Common Tangents Internal
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Common Tangents External
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If a line (segment or ray) is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. Point of Tangency More Pythagorean Theorem type problems! Yeah!!
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a 2 + b 2 = c 2 x = 15 9 2 + 12 2 = x 2
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a 2 + b 2 = c 2 RQ = 16 12 2 + (QR) 2 = (8+12) 2 12 2 + (QR) 2 = 20 2
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No a 2 + b 2 = c 2 ?
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r 2 + 24 2 = (r + 16) 2 r = 10 r 2 + 576 = r 2 + 32r + 256 320 = 32r
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A green on a golf course is in the shape of a circle. Your golf ball is 8 feet from the edge of the green and 32 feet from a point of tangency on the green. a)What is the radius? b) How far is your ball from the cup at the center? x = 60 ft. x = 68 ft.
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R S T If two segments from the same exterior point are tangent to a circle, then they are congruent. Party hat problems!
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R S T
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R S T
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A C B
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A C E B D P
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T S Q P N R
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