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Circle Proofs

Circle Proofs. A. J. C. B. JA  JB. Tangents in Proofs. Given AC and BC are tangent to circle J at A and B respectively, prove AC  BC. AC and BC are tangent to circle J . Given. AC  JA and BC  JB.

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Circle Proofs

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  1. Circle Proofs

  2. A J C B JA  JB Tangents in Proofs Given AC and BC are tangent to circle J at A and B respectively, prove AC  BC AC and BC are tangent to circle J Given AC  JA and BC  JB Theorem 12-2 (A line tangent to a circle is  to the radius at the point of tangency.) JAC and JBC are right triangles Definition of Right Triangle All radii of a circle are  JC  JC Reflexive Property JAC  JBC Hypotenuse-Leg Theorem AC  BC CPCTC

  3. A 10 cm D 15 cm F O B 8 cm E C Example 5 Circle O is inscribed in ABC. Find the perimeter of ABC. AD = AF = 10 cm BD = BE = 15 cm CF = CE = 8 cm The perimeter is AD + AF + BD + BE + CF + CE perimeter = 10 + 10 + 15 + 15 + 8 + 8 = 66 cm

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