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Tangent Properties Calculator

Online tangent-length calculator. Enter the distance d from an outside point to the center and the radius r to get the tangent length √(d²−r²)—great for circle power.

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Tangent length = √(D² − r²)
External point to center
Radius

📖 Tutorial | Tangent

1. Definition
A tangent meets the circle at exactly one point.
2. Formula & Notation
DExternal point to center
rRadius
tLength, √(D²−r²)
3. Properties & Laws
  • Perpendicular to the radius at contact;
  • Two tangents from one point equal;
  • t=√(D²−r²);
  • The center line bisects their angle.
4. Steps
  1. Enter D, r (D>r);
  2. Click "Find Tangent";
  3. Or click "Load Example".
5. Worked Examples
Example: D=13, r=5.
Solution: t = √144 = 12.
6. Common Pitfalls
D must exceed r;
Tangent is perpendicular;
Two tangents equal.

❓ FAQ | Tangent

Property?
Perpendicular to radius at contact.
Length?
√(D²−r²).
D=13,r=5?
12.
Two tangents?
Equal.
Test for tangent?
Through radius endpoint, perpendicular.
Intersections?
Exactly one.