Question

in this activity you will: apply properties of tangents. determine if a line is tangent to a circle. find the perimeter of a polygon circumscribed about a circle. value: 2 determine if line ab is tangent to the circle. a. tangent b. not tangent

Explanation:

Step1: Recall tangent - radius property

If a line is tangent to a circle, then the radius drawn to the point of tangency is perpendicular to the tangent line. We can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) to check if the triangle formed by the radius, the line segment from the center of the circle to the external - point, and the line in question is a right - triangle.
Let the radius of the circle \(r = 8\), the distance from the external point \(B\) to the point of intersection of the line and the circle be \(12\), and the distance from the external point \(B\) to the center of the circle (hypotenuse) be \(20\).

Step2: Apply the Pythagorean theorem

If the triangle is a right - triangle, then \(8^{2}+12^{2}\) should be equal to \(20^{2}\). Calculate \(8^{2}=64\), \(12^{2}=144\), and \(8^{2}+12^{2}=64 + 144=208\). Calculate \(20^{2}=400\). Since \(8^{2}+12^{2}
eq20^{2}\), the angle between the radius and line \(AB\) is not a right - angle.

Answer:

b. Not tangent