1. ## locus of orthocentre

ABC is an acute angled triangle. P is a point on BC. X and Y lie on AB and AC respectively such that XP is perpendicular to AB and YP is perpendicular to AC. what is the locus of the orthocentre of the triangle AXY as P moves on BC?

2. Originally Posted by abhishekkgp
ABC is an acute angled triangle. P is a point on BC. X and Y lie on AB and AC respectively such that XP is perpendicular to AB and YP is perpendicular to AC. what is the locus of the orthocentre of the triangle AXY as P moves on BC?
As a starter so that you know what you should get ...

3. Originally Posted by earboth
As a starter so that you know what you should get ...
thats right but how do i proceed from here?

4. If you observe the image you can see that x, P,y and the orthocenter form a parallelogram. As P changes its position, the shape of the parallogram changes. When P is at B and C, it becomes a straight line. So the red line in the image is the locus of the orthocenter.

5. Originally Posted by sa-ri-ga-ma
If you observe the image you can see that x, P,y and the orthocenter form a parallelogram. As P changes its position, the shape of the parallogram changes. When P is at B and C, it becomes a straight line. So the red line in the image is the locus of the orthocenter.
so is the locus a STRAIGHT line?

6. Yes.