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Circle Intersection Calculator

Geometry

overlap area & common chord

Quick Answer

Circle Intersection Calculator: overlap area & common chord. Circle Intersection Calculator uses standard geometry formulas to compute accurate results instantly.

Two circles

cm
cm
cm
PositionIntersecting · 2 intersection(s)
Overlap area8.85 cm²
Common chord6.5 cm

How it works

  1. 1Compare d=10 with |r₁−r₂| and r₁+r₂ to classify the position
  2. 2θ₁=2·arccos((r₁²+d²−r₂²)/2r₁d) (θ₂ likewise); overlap = two sectors − two triangles
  3. 3Chord = (1/d)·√[(d²−(r₁−r₂)²)·((r₁+r₂)²−d²)] = 6.5 cm
The position depends on d vs the radii: d>r₁+r₂ separate, d=r₁+r₂ externally tangent, |r₁−r₂|<d<r₁+r₂ intersecting (2 points), d=|r₁−r₂| internally tangent, d<|r₁−r₂| contained (d=0 concentric). Use an epsilon (1e-9) for float equality or tangent cases get missed. Overlap = the smaller circle when contained; tangent circles share zero area but one point. For intersection coordinates, subtract the two circle equations to get the radical line.

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How to Use

  1. Enter known values: fill sides, radius or angles in the Circle Intersection Calculator.
  2. Auto-solve the rest: all unknowns are solved instantly — no manual derivation.
  3. See formula and steps: the result panel shows the formula used and the substitution.
  4. Try another case: change any known value to solve again.

Key Points

  • Circle Intersection Calculator is a free online geometry tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: overlap area & common chord.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Circle Intersection Calculator formula

Circle Intersection Calculator uses standard geometry formulas to compute accurate results instantly.

FAQ

How do I use the Circle Intersection Calculator?
Open the page and fill in the input fields — results update automatically. overlap area & common chord.
Are the results accurate?
Yes. Standard formulas and conversion factors are used and verified.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. Everything runs locally in your browser.

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Source & Updates

Based on standard Euclidean geometry formulas. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

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Cite this page: YiJianSuan. Circle Intersection Calculator[EB/OL]. https://www.yijiansuan.com/en/c/geometry/two-circles

Results provided by this tool are for reference only and do not constitute professional advice.