# 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

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