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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