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1.5 – Special Points in Triangles

1.5 – Special Points in Triangles. Incenter. Incenter: the center point of the inscribed circle Inscribed circle : the circle inside the triangle that just touches all 3 sides. Circumcenter. Circumcenter : the center point of the circumscribed circle

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1.5 – Special Points in Triangles

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  1. 1.5 – Special Points in Triangles

  2. Incenter • Incenter: the center point of the inscribed circle • Inscribed circle: the circle inside the triangle that just touches all 3 sides

  3. Circumcenter • Circumcenter: the center point of the circumscribed circle • Circumscribed circle: the circle that is around the triangle that just touches all 3 corners

  4. CONJECTURE • A statement that you think is true • An educated guess based on observation • Sometimes becomes a mathematical discovery

  5. CONJECTURE 1 • The bisectors of the 3 angles of a triangle will intersect at the incenter, which will be the center of an inscribed circle (a circle INSIDE a triangle)

  6. IN (touching each side)

  7. CONJECTURE 2 • The perpendicular bisectors of the 3 sides of a triangle will intersect at the circumcenter, which will be the center of a circumscribed circle (a circle OUTSIDE a triangle)

  8. OUT (just touching each vertex)

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