Circumcentre and Incentre
Centres of the circumscribed and inscribed circles.
Key idea
Centres of the circumscribed and inscribed circles.
In depth
The circumcentre is where the perpendicular bisectors meet, equidistant from the vertices. The incentre is where the angle bisectors meet, equidistant from the sides. They are centres of the circumscribed and inscribed circles.
Worked example
A right triangle has its circumcentre at the midpoint of the hypotenuse.
Real-world uses
- Finding the centre of a circle through three towers
- Placing a fountain equidistant from three sides
Common mistake
Confusing which lines produce which centre.
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 Circumcentre and Incentre?
Centres of the circumscribed and inscribed circles. It is a topic at the advanced level in Geometry.
Where is Circumcentre and Incentre used in real life?
Real-world examples: Finding the centre of a circle through three towers; Placing a fountain equidistant from three sides.
What should I learn before Circumcentre and Incentre?
Make sure you are comfortable with Medians and Centroid, the previous topic in Geometry.
What is a common mistake with Circumcentre and Incentre?
Confusing which lines produce which centre.
How can I practise Circumcentre and Incentre?
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 Circumcentre and Incentre?
Move on to Orthocentre next.
Related advanced topics in Geometry
- Heron’s Formula – Triangle area from three sides.
- Regular Polygon Area – Use apothem and perimeter.
- Arc Length of a Circle – Part of the circumference.
- Sector Area – Part of the circle’s area.
- Central and Inscribed Angles – An inscribed angle is half the central angle on the same arc.
- Chord and Tangent Properties – A tangent is perpendicular to the radius at the point of contact.