Simson Lines

Simson LinesAbella | Caresosa | pasigaySimson linethe line joining the feet of the perpendiculars let fall from any point on the circumcircle of a triangle upon the sides of the triangle

Prove"The simson line of diametrically opposite points on the circumcircle are perpendicular to each other and meet on the nine-point circle."

Darker Version

Darker VersionWhat can we notice about

is cyclic

Darker Version

Because they are subtended by the same arc

(subtended by the same arc)

Conclusion: