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True or false the center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle

Respuesta :

The answer is TRUE!!!!!
frika

Answer:

True

Step-by-step explanation:

Consider triangle ABC inscribed in the circle with center at point O. Point O is a point of intersection of perpendicular bisectors of sides AC, AB and BC. According to the attached diagram, points E, F and G are midpoints of sides BC, AC and AB, respectively.

Then

  • EB=EC;
  • FC=FA;
  • GA=GB.

Since segments OE, OF and OG are perpendicular bisectors of sides BC, AC and AB, then

  • m∠OBE=m∠OCE=90°;
  • m∠OCF=m∠OAF=90°;
  • m∠OBG=m∠OAG=90°.

You get three pairs of congruent triangles:

  1. ΔOBE≅ΔOCE;
  2. ΔOCF≅ΔOAF;
  3. ΔOBG≅ΔOAG.

This gives you that

[tex]OB=OC=OA.[/tex]

Each of these segments is a radius of the circumscribed circle about a triangle ABC, then the center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle.

Ver imagen frika