Let the three heights of △ ABC BE AD, BE and CF, where D, E and F are vertical, orthocenter is H, and opposite sides of angles A, B and C are a, b and c respectively

1, trigonometric orthocenter in trigonometric; trigonometric orthocenter trigonometric orthocenter; Obtuse trigonometric orthocenter outside trigonometric.

2, trigonometric orthocenter is the trigonometric orthocenter; trigonometric orthocenter; trigonometric orthocenter; 3, orthocenter H about the trilateral symmetry points, are on the △ABC outer circle.

4, △ABC, there are six groups of four-point common circle, there are three groups (each group of four) similar trigonometric, and AH·HD=BH·HE=CH·HF.

Any point of the four points 5, H, A, B, C is the vertex of the remaining three trigonometric orthocenter (and such four points are called the one-orthocenter group).

6, △ABC, △ABH, △BCH, △ACH peripheral circles are equal circles.

7. In a non-right angled trigonometric, if the straight lines where AB and AC cross H straight line are P and Q respectively, AB/AP·tanB+AC/AQ·tanC=tanA+tanB+tanC.

8, trigonometric any vertex to the orthocenter distance, be tantamount to the outer center to the opposite side distance 2 times.

9. Let O and H be △ABC outer center and orthocenter respectively, then ∠BAO=∠HAC, ∠ABH=∠OBC, ∠BCO=∠HCA.

10, acute Angle trigonometric orthocenter distance sum to three vertices be tantamount to its inner circle and outer circle radius sum 2 times.

11, trigonometric orthocenter is vertical trigonometric heart; An acute trigonometric corner is enclosed in a trigonometric corner (the apex is on the edge of the original trigonometric), and the shortest is the vertical trigonometric perimeter.

(p>12) Simson's theorem (Simson line) : The sufficient and necessary condition for a vertical line drawn from a point to trigonometric three sides is that the point falls on the trigonometric outer circle.

13, Let there be a point P in acute Angle △ ABC, then P is orthocenter sufficient and necessary condition is PB*PC*BC+PB*PA*AB+PA*PC*AC=AB*BC*CA.