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36. Tangents to Circles
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Tangents to Circles Std – MM2G3 – Understand properties of circles
EQ – What are the rules for tangents?
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Fact #1 A tangent line is ALWAYS perpendicular to the radius of the circle drawn to the point of tangency. radius 90 degrees = perpendicular tangent
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What this fact means…. What this means is that you can make a right triangle and use the pythagorean theorem to find distances. The right angle will always be the one on the outside of the circle radius tangent
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Example – Find the length of AC
a2 + b2 = c2 = c2 = c2 89 = c2 = c
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Example – find x ANSWER: x = 8
Since a radius of the circle is 5, any radius is 5… Since it is a radius drawn to a point of tangency, it is perpendicular to the tangent. 5 a2 + b2 = c2 = c2 = c2 169 = c2 13 = c ? This whole length is 13. x + 5 = 13 x = 8 5 12 ANSWER: x = 8
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Example Find KY a2 + b2 = c2 102 + b2 = 242 100 + b2 = 576 476 = b2
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Example Does this picture show a tangent? a2 + b2 = c2
It must satisfy Pythagorean Theorem a2 + b2 = c2 = (18+7)2 625 = 625 Yes!
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“Party Hat” Theorem If two segments from the same exterior point are tangent to a circle, then they are congruent. tangent #1 exterior point tangent #2 They are congruent.
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What this fact means…. What this means is that you can set the 2 tangents equal to each other Tangent 1 = tangent 2 tangent #1 tangent #2
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Example exterior point x=14.
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Example Find length of tangent
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Visible Horizon-Using tangents in navigation
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