Secants and tangents

Idea

The same point $P$ outside the unit circle, with a horizontal secant through $A$ and $B$. This page keeps that horizontal secant and swaps the other line between a second secant and the upper tangent. It is not the two-secants page, which has two secants and no tangent, and not the tangent-and-a-secant page, which has a slanted secant plus the upper tangent and no horizontal line.

$PA$ is the external part and $PB$ is the whole secant. $PT$ is the tangent segment. Both cases equal the power of that point. Each number is computed from the intersection coordinates. Values are shown to three decimal places, rounded half up. The angle is fixed; only the point moves.

Interaction

• Position: move the exterior point; the two lengths change with it
• Two secants: show the horizontal secant and another secant
• Tangent: show the horizontal secant and the upper tangent

Suggested order: two secants, then the tangent.

What to notice

• At the same point, both cases read the same number.
• What changes is two intersections or one point of tangency.
• That shared number grows only as the point moves farther from the center.

Related

• Two secants
• Tangent and a secant

Further reading

• Power of a point (Wikipedia)