CPM Homework Help : PC Problem 8-73

Two tangent lines are drawn on the circle $x^{2} + y^{2} = 25$ , one at the point $\left(4, 3\right)$ and the other at the point $\left(−3, 4\right)$ . What is the point of intersection for the two tangent lines?

Step 1:

Find the equations of the tangents by using the point-slope form.
The slopes of the tangents are the reciprocals of the slopes of the corresponding radii multiplied by −1.

Step 2:

Set the two equations equal to each other and solve for the coordinates of the intersection.

Answer:

(1,7)

Use the eTool below to help solve this problem by graphing.
Click the link at right for the full version of the eTool: 8-73 HW eTool