The Secant Theorem equations computes the length of a line from a point outside a circle to a tangent point on the circle based on the Tangent-Secant Theorem.
INSTRUCTIONS: Choose units and enter the following:
- (r) Radius of the circle, where r = 1/2 GE
- (DE) Distance of point D outside the circle
Distance to Tangent (DC): The calculator returns the distance in meters. However, this can be automatically converted to compatible units via the pull-down menu.
The Math / Science
The Tangent-Secant Theorem represents that if a line from a point D outside a circle intersects the circle at exactly one point C (in other words DC is tangent to the circle) and a secant (a line intersecting the circle at two points) from the same external point D meets the circle at points G and E respectively, then DC2 = DG × DE as shown in the diagram.
Since the radius of the circle, r = 1/2 GE, then DG = 2r + DE
So, DC2 = (2r +DE) * DE
`DC = sqrt((2r +DE) * DE)`