CPM Homework Help : PC3 Problem 11-72

Two lines are drawn tangent to 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?

Hint:

Draw a diagram. Recall that a line tangent to a circle is perpendicular to the radius at that point.

More Help:

Circle, center at the origin, passing through the points (5, comma 0), & (0, comma 5), with dashed radii, to the points (negative 3, comma 4), & (4, comma 3), & bold lines through the 2 points, tanget to the circle.