Circles
Class 10 · Mathematics
3 ideas in Class 10 Mathematics, explained in plain words, with games and quizzes to practise.
Lines and Tangents to a Circle
Part of: Lines and Tangents to a Circle
A line may miss a circle, cut it at two points as a secant, or meet it once as a tangent. The single shared point is the point of contact.
Why it matters. Tangent properties help reason about circles, contact and equal distances in geometric constructions.
Try it in two minutes
- Count how many times the line meets the circle.
- Connect a contact point to the centre with a radius.
- Use perpendicularity or equal tangent lengths to prove a result.
Try at home. Place a round lid on paper and sketch a line that touches its edge at one point, then draw the radius to that point.
Radius and Tangent Properties
Part of: Radius and Tangent Properties
The radius to a tangent's point of contact is perpendicular to the tangent. The centre-to-line distance is shortest along this perpendicular.
Why it matters. Tangent properties help reason about circles, contact and equal distances in geometric constructions.
Try it in two minutes
- Count how many times the line meets the circle.
- Connect a contact point to the centre with a radius.
- Use perpendicularity or equal tangent lengths to prove a result.
Try at home. Place a round lid on paper and sketch a line that touches its edge at one point, then draw the radius to that point.
Tangents from an External Point
Part of: Tangents from an External Point
Two tangents drawn from the same external point to a circle have equal lengths. The centre and contact points also form useful congruent right triangles.
Why it matters. Tangent properties help reason about circles, contact and equal distances in geometric constructions.
Try it in two minutes
- Count how many times the line meets the circle.
- Connect a contact point to the centre with a radius.
- Use perpendicularity or equal tangent lengths to prove a result.
Try at home. Place a round lid on paper and sketch a line that touches its edge at one point, then draw the radius to that point.
What your child will practise
- Lines and Tangents to a Circle: Candy Puzzle (Clue Puzzle)
- Lines and Tangents to a Circle: Number Quest (Match It Up)
- Lines and Tangents to a Circle: Space Quick Fire (Quick Fire)
- Radius and Tangent Properties: Ocean Quick Fire (Quick Fire)
- Tangents from an External Point: Mission Control Quest (Collect the Answer)
- Quiz: Lines and Tangents to a Circle (8 questions)
- Quiz: Radius and Tangent Properties (8 questions)
- Quiz: Tangents from an External Point (8 questions)