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Keith
Keith
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Let a Triangle $\triangle ABC$ be inscribed in a circle, along the arc $\overset{\frown}{BC}$ lies a point $P$ such as, $BP=4\sqrt{2}$.

enter image description here

Compute the distance between the two orthocenters of the triangles $\triangle ABC$ and $\triangle APC $.

  • As you can see form the picture above the segment $BP$ seems to be parallel with "AC""$H_1H_2$". But I don't know how to prove it. I believe something about the nine point circle might be useful.

Let a Triangle $\triangle ABC$ be inscribed in a circle, along the arc $\overset{\frown}{BC}$ lies a point $P$ such as, $BP=4\sqrt{2}$.

enter image description here

Compute the distance between the two orthocenters of the triangles $\triangle ABC$ and $\triangle APC $.

  • As you can see form the picture above the segment $BP$ seems to be parallel with "AC". But I don't know how to prove it. I believe something about the nine point circle might be useful.

Let a Triangle $\triangle ABC$ be inscribed in a circle, along the arc $\overset{\frown}{BC}$ lies a point $P$ such as, $BP=4\sqrt{2}$.

enter image description here

Compute the distance between the two orthocenters of the triangles $\triangle ABC$ and $\triangle APC $.

  • As you can see form the picture above the segment $BP$ seems to be parallel with "$H_1H_2$". But I don't know how to prove it. I believe something about the nine point circle might be useful.
Source Link
Keith
Keith
  • 1.2k
  • 1
  • 7
  • 17

Distances between two orthocenters

Let a Triangle $\triangle ABC$ be inscribed in a circle, along the arc $\overset{\frown}{BC}$ lies a point $P$ such as, $BP=4\sqrt{2}$.

enter image description here

Compute the distance between the two orthocenters of the triangles $\triangle ABC$ and $\triangle APC $.

  • As you can see form the picture above the segment $BP$ seems to be parallel with "AC". But I don't know how to prove it. I believe something about the nine point circle might be useful.