Tangent Line Calculator
Calculate tangent lines from an external point to a circle. Find tangent length using the formula: tangent = √(d² - r²).
Circle Properties
External Point
Related Calculators
Frequently Asked Questions
What is a tangent line to a circle?
A tangent line touches the circle at exactly one point and is perpendicular to the radius at that point of contact.
What is the formula for tangent length?
t = √(d² - r²), where t is the tangent length, d is the distance from the external point to the center, and r is the radius. This comes from the Pythagorean theorem.
How many tangent lines can be drawn from an external point?
Exactly two tangent lines can be drawn from any external point to a circle, and they have equal length.
Why is the tangent perpendicular to the radius?
The radius to the point of tangency is perpendicular to the tangent line. This is a fundamental property that creates a right triangle used in tangent length calculations.
What if the point is inside the circle?
No tangent lines can be drawn from a point inside the circle. The point must be outside (distance from center greater than radius).
What if the point is on the circle?
If the point is exactly on the circle, there is exactly one tangent line at that point, and the tangent length is zero.
Are both tangents from an external point equal?
Yes, the two tangent segments from an external point to a circle always have equal length. This is a useful property in geometric proofs.
Where are tangent calculations used?
Tangent calculations are used in optics (light reflection), road design (curves and transitions), robotics (path planning), and computer graphics.