Orthocentre
Intersection of triangle altitudes.
Key idea
Intersection of triangle altitudes.
In depth
The orthocentre is where the three altitudes meet. It can lie outside an obtuse triangle and coincides with the right-angle vertex in a right triangle.
Worked example
In a right triangle with the right angle at C, the orthocentre is C.
Real-world uses
- Analysing triangle structures in engineering
- Geometry problems in competitions
Common mistake
Assuming it is always inside the triangle.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Orthocentre?
Intersection of triangle altitudes. It is a topic at the expert level in Geometry.
Where is Orthocentre used in real life?
Real-world examples: Analysing triangle structures in engineering; Geometry problems in competitions.
What should I learn before Orthocentre?
Make sure you are comfortable with Circumcentre and Incentre, the previous topic in Geometry.
What is a common mistake with Orthocentre?
Assuming it is always inside the triangle.
How can I practise Orthocentre?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Orthocentre?
Move on to Euler Line next.
Related expert topics in Geometry
- Power of a Point – For a point and a circle, products of segment lengths along secants are equal.
- Cyclic Quadrilaterals – Opposite angles of a quadrilateral inscribed in a circle sum to 180°.
- Cavalieri’s Principle – Solids with equal cross-sectional areas at every height have equal volume.
- Area by Coordinates (Shoelace) – Area of a polygon from vertices.
- Parabola (Geometric Definition) – Points equidistant from a focus and a directrix.
- Ellipse – Sum of distances to two foci is constant.