We can use the theorems we learned about in the video to solve geometric problems involving circles and tangent lines. Work through the following tabs to learn more about these kinds of problems.
Example 1
Example 2
AB and AC are tangent to circle S. If the measure of line segment AB is equal to 15 cm and the measure of line segment AC is equal to 2x - 5, what is the value of x? Solve this problem.
Since AB and AC are tangent to circle S and they originate form a point outside of the circle, the line segments AB and AC are congruent. We can write and solve the following equation:
2x - 5 = 15
2x = 20
x = 10
Assume AB is tangent to circle C. AC is a radius of circle C. Using the image above find the length of the missing side of triangle ABC. Think about this problem and calculate an answer.
AB is a tangent line, AC is a radius, and point A is the point of tangency. That means AB and AC are perpendicular. This creates a right triangle ABC with a right angle at A. We can use the Pythagorean Theorem to solve this problem.
\(\small\mathsf{ 12^{2}+16^{2}=x^{2} }\)
\(\small\mathsf{ 144+256=x^{2} }\)
\(\small\mathsf{400=x^{2} }\)
x = 20
Now, go on to the next page to practice these kinds of problems on your own.
