Sample solution here .
- Let be a triangle with vertices at , , and . Let be as defined in today’s post.
- Find the coordinates of
- Verify that , where is the circumradius.
This is a paragraph.
Observe that the given triangle is right-angled at . Further, in a right triangle, the symmedian point is the midpoint of the right-angled vertex and the foot of the altitude from the right-angled vertex. In a previous post, we found the foot of the altitude from to be . Thus, the symmedian point in this case is .
We have , , , and .
Explicit calculation gives
Thus and divide harmonically, since: