# For the circle, #(x+1)^2+(y+2)^2=25# What is the length of the tangent to the circle from the point #(6,4)#?

##### 1 Answer

The length of the tangent to the circle from the point

#### Explanation:

The circle

As the length of the tangent from the external point, radius to the point at which tangent touches circle and line joining external point to center of circle form a right angle.

Now radius is

and hence using Pythagorus theorem, lengt of tangent is

graph{((x+1)^2+(y+2)^2-0.03)((x+1)^2+(y+2)^2-25)((x-6)^2+(y-4)^2-0.03)=0 [-10, 10, -4.8, 5.2]}

Obsserve that the length of the tangent to a circle