Orthocenter

The three altitudes meet at the orthocentre H. It is inside an acute triangle, at the right-angle vertex of a right triangle, and outside an obtuse triangle.

HOrthocenter

📐 Formula

H = intersection of the altitudes; H = 3G − 2O

✏️ Worked example

For A(−3, −2), B(3, −2), C(1, 3), H = (1, −0.4).

🌍 Where it is used

Triangle geometry and the Euler line.

❓ Quick check

Orthocentre of a right triangle is at…

🏋️ Practice

EasyWhere are the altitudes of an equilateral triangle?

Answer: Along the medians

MediumFor an obtuse triangle, is H inside?

Answer: No, outside

ChallengeWhat meets at H?

Answer: The three altitudes