proof of Simson’s line
Since is perpendicular to and is perpendicular to the point lies on the circumcircle of .
This implies that , and are all cyclic quadrilaterals.
Since is a cyclic quadrilateral,
Also is a cyclic quadrilateral, therefore
(opposite angles in a cyclic quarilateral are supplementary).
From these two, we get
Subracting , we have
Now, since is a cyclic quadrilateral,
also, since is a cyclic quadrilateral,
Combining these two results with the previous one, we have
This implies that the points are collinear.
|Title||proof of Simson’s line|
|Date of creation||2013-03-22 13:08:26|
|Last modified on||2013-03-22 13:08:26|
|Last modified by||giri (919)|