Calculate length of tangent from external point
The tangent to a circle is perpendicular to the radius at the point of tangency. This forms a right triangle where the distance from the center is the hypotenuse.t = √(d² - r²)
Measure or determine the radius of the circle from the center to the edge.
Why: The radius is essential for the Pythagorean relationship. Without it, you cannot calculate the tangent length.
Measure the distance from the circle's center to the external point where the tangent originates.
Why: The tangent only exists when this distance exceeds the radius. This ensures the external point is actually outside the circle.
Check that the distance from center is greater than the radius (d > r).
Why: A tangent can only be drawn from an external point. If d ≤ r, the point is inside or on the circle, making the calculation impossible.
Use the formula t = √(d² - r²) to calculate the tangent length.
Why: The radius, tangent, and distance form a right triangle. The tangent is perpendicular to the radius, so the Pythagorean theorem applies directly.
Verify the result is positive and less than the distance. Document both the radius and distance used.
Why: The tangent length must satisfy 0 < t < d. Documenting inputs prevents recalculation errors and validates your measurements.
Drawing a Tangent to a Fountain