SimsonProperty2

The angle of two Simson Lines

Consider triangle t=ABC and a point D on its circumcircle (c) and a second point E on (c) at central angle (2phi) from D. Project D, E on the sides of (t) and define the Simson lines S(D), S(E) (see Simson.html ). Then the angle of the two Simson lines S(D) and S(E) is (phi) i.e. half the angle of the central angle of D and E.

The proof follows from SimsonProperty.html , where it is proved that lines AH, AI are parallel to the corresponding Simson lines S(D) and S(E) respectively. Then it is created the isosceles trapezium DEIH, where angle(EOD) is the central angle (2phi) and angle(IAH) is viewing arc(IH) = arc(DE) from point A on the circumference of (c).

See the file SimsonDiametral.html where is discussed the case of diametral D and E i.e. of phi being equal to a right angle.

The angle of two Simson Lines

See Also