Unformatted text preview: b a c A B C O D r E F Figure 2.5.6 Inscribed circle for △ ABC Let r be the radius of the inscribed circle, and let D , E , and F be the points on AB , BC , and AC , respectively, at which the circle is tangent. Then OD ⊥ AB , OE ⊥ BC , and OF ⊥ AC . Thus, △ OAD and △ OAF are equivalent triangles, since they are right triangles with the same hypotenuse OA and with corresponding legs OD and OF of the same length r . Hence, ∠ OAD = ∠ OAF , which means that OA bisects the angle A . Similarly, OB bisects B and OC bisects C . We have thus shown: For any triangle, the center of its inscribed circle is the intersection of the bisectors of the angles....
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 Fall '11
 Dr.Cheun
 Calculus, Angles, Pythagorean Theorem, Right triangle, triangle

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