Chord and Tangent Properties
A tangent is perpendicular to the radius at the point of contact.
Key idea
A tangent is perpendicular to the radius at the point of contact.
In depth
A tangent is perpendicular to the radius at the point of contact. Tangents from one outside point have equal length. A perpendicular from the centre bisects a chord.
Worked example
Radius 5, tangent length from a point 13 from the centre: √(13² − 5²) = 12.
Real-world uses
- Designing a wheel rim or a gear where a line just touches a circle
- Road curves in engineering
Common mistake
Forgetting the right angle between tangent and radius.
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 Chord and Tangent Properties?
A tangent is perpendicular to the radius at the point of contact. It is a topic at the advanced level in Geometry.
Where is Chord and Tangent Properties used in real life?
Real-world examples: Designing a wheel rim or a gear where a line just touches a circle; Road curves in engineering.
What should I learn before Chord and Tangent Properties?
Make sure you are comfortable with Central and Inscribed Angles, the previous topic in Geometry.
What is a common mistake with Chord and Tangent Properties?
Forgetting the right angle between tangent and radius.
How can I practise Chord and Tangent Properties?
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 Chord and Tangent Properties?
Move on to Power of a Point 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.
- Cones – Volume and surface area of a cone.