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Homework Review

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CCGPS Geometry Day 26 (9-12-13) 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 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 E B D P

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T S Q P N R

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Intersections of Circles and Tangent Segments. R S T If two segments from the same exterior point are tangent to a circle, then they are congruent. Party.

Intersections of Circles and Tangent Segments. R S T If two segments from the same exterior point are tangent to a circle, then they are congruent. Party.

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