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  "body": "\n## Definition\n\nLet $C$ be a [[circle|060W5CBZP6]] in the Euclidean plane $\\mathbb{R}^2$, and let $T$ be a point of $C$.\nA [[line|0MP9BCF6DP]] $\\ell$ is tangent to $C$ at $T$ if $\\ell \\cap C = \\{T\\}$. The point $T$ is the point of tangency.\n\n## Remarks\n\nA line meets a circle in two points, in one point or in no point. A line with two common points is a secant line.\nFor the circle $(x - a)^2 + (y - b)^2 = r^2$ and a point $(x_1, y_1)$ on it, the tangent at this point has the equation $(x - x_1)(x_1 - a) + (y - y_1)(y_1 - b) = 0$.\nThe tangent at $T$ is the line through $T$ perpendicular to the radius to $T$. See [[a tangent is perpendicular to the radius|031JV5S54D]].\nFrom a point outside the circle there are exactly two tangent lines to the circle.\n\n## Explanations\n\n### L1 human\n\nA tangent line just touches a circle at one point and stays outside the circle. For the unit circle, the line $y = 1$ is tangent at $(0, 1)$. The line $y = 0$ is not tangent: it meets the circle at $(1, 0)$ and at $(-1, 0)$.\n",
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