2.  One way we can prove that a line is tangent to a circle is to use the converse of the Pythagorean Theorem.

3.  The converse of the Pythagorean Theorem states that for any triangle with side lengths a, b, and c, such that a 2 +b 2 =c 2, then the angle between a and b will be 90 degrees.

4. a b c A C B

5.  Notice that side length a happens to be the radius of the circle.  Because the radius of the circle is perpendicular to the line intersecting the circle at the point of tangency, that line must be tangent to the circle.

6.  Using this information we can determine if a line, which segment b is a portion of, is tangent to a circle or not.

7. Determine if the orange segment in the triangle ABC is tangent to the circle. 11 4 12 B A C

8.  In order to check the converse of the Pythagorean Theorem, simply check whether or not the Pythagorean Theorem holds true.

9.  If the Pythagorean Theorem holds true, then the orange segment will be tangent to the circle.  If the Pythagorean Theorem does not hold true, then the orange segment will not be tangent to the circle.

10. 11 4 12 Substitute in values Simplify Check to see if statement is true. B A C

11.  137 does not equal 144, therefore the Pythagorean Theorem failed.  This means that the angle between the radius and the orange segment is not 90 degrees.

12.  Since the angle between the radius and the orange segment is not 90 degrees, the orange segment cannot be tangent to the circle.