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User:Bawolff/math steps

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Let be a triangle. The altitudes and intersect at . We will show that also is perpendicular to , i.e. an altitude of .

  • The quadrilateral is cyclic, because . So, also (subtended by the same arc).
  • The quadrilateral is cyclic because opposite angles and are supplementary (). So, angles and are equal.
  • The angles and are equal as vertical angles, i.e. . In the right triangle , we have that , therefore in the triangle it holds that .

We conclude that, ...


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