Circles notes
OpenThe 4 formulas you need for Circles, on one page.
For explanations and lectures, see the full topic page. Then test yourself with 1 JEE Main 2026 PYQs.
Maths · printable
Circles: One-Page Formula Sheet
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Last updated: 26 October 2026
Formula sheet
Circles formulas
Circles — formula sheet
Formulas
- Radius r = √(g² + f² − c)
- Tangent at (x₁, y₁): T = 0
- Length of tangent = √S₁
- Orthogonal circles: 2g₁g₂ + 2f₁f₂ = c₁ + c₂
Key ideas
- General form x² + y² + 2gx + 2fy + c = 0, centre (−g, −f)
- Line is tangent if distance from centre = radius
- Two circles: compare distance between centres with radii
- Radical axis: S₁ − S₂ = 0
Traps to avoid
- Sign of centre coordinates
- Forgetting the condition r² > 0
- Wrong formula for common tangents count
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FAQs
Frequently asked questions
Where can I get a Circles formula sheet PDF for free?
On this page. Use the print button and choose 'Save as PDF'.
How should I use a formula sheet?
Read it once a day for a week, then cover it and write the formulas from memory. Revise only the ones you missed.