Length of Tangent to a Circle Formula From an External Point

Here you will learn what is the length of tangent to a circle formula from an external point with example.

Let’s begin –

Length of Tangent to a Circle Formula

The length of tangent drawn from point (\(x_1,y_1\)) outside the circle

S = \(x^2 + y^2 + 2gx + 2fy + c\) = 0 is,

\(\sqrt{S_1}\) = (\(\sqrt{{x_1}^2 + {y_1}^2 + 2gx_1 + 2fy_1 + c}\))

Note : When we use this formula the coefficient of \(x^2\) and \(y^2\) must be 1.

Also Read : Equation of Pair of Tangents to a Circle

Example : Find the length of tangent from the point (9, 12) to the circle \(2x^2 + 2y^2 – 6x + 8y + 10\) = 0

Solution : Dividing the given equation of circle by 2, we get the standard form,

\(x^2 + y^2 – 3x + 4y + 5\) = 0

Now, by using above formula the length from (9, 12) is

\(\sqrt{9^2 + 12^2 + (-3)(12) + 4(9) + 10}\) = \(\sqrt{81 + 144 – 36 + 36 +10}\) = \(\sqrt{235}\).

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