O is the orthocenter of the triangle ABC. The lengths centered around point O and the lengths of the orthic triangle DEF are solved in terms of the side lengths. The area of the triangle is found with Heron’s formula. #math #maths #mathemati cs #geometry #trigonometry

The orthic triangle is the triangle made by connecting the points where each altitude meets their corresponding side. Since orthocenter is the common meeting point of the quadrilaterals, then three cyclic quadrilaterals are formed, so Ptolemy’s theorem can be used to find the lengths of the sides o

In any acute triangle ABC, the distances from the orthocenter (where the altitudes meet) to the vertices are of the form 2R × cos Ε, where E is one of the angles of the triangle. R is the length of the circumradius of the triangle. #math #maths #mathematics #geometry #trigonometry