Question

value: 2
determine if line ab is tangent to the circle.
12
20
14
a. tangent
b. not tangent

Explanation:

Step1: Recall the tangent - radius property

If a line is tangent to a circle, then it is perpendicular to the radius at the point of tangency. We can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse of a right - triangle and \(a\) and \(b\) are the legs.

Step2: Identify the sides of the triangle

Let the radius of the circle be \(r = 14\), the length of \(AB=12\), and the distance from the center of the circle to point \(B\) be \(d = 20\). If \(AB\) is tangent to the circle, then the triangle formed by the radius, the tangent line \(AB\), and the line from the center of the circle to point \(B\) is a right - triangle.

Step3: Apply the Pythagorean theorem

Check if \(12^{2}+14^{2}=20^{2}\). Calculate \(12^{2}=144\), \(14^{2}=196\), and \(20^{2}=400\). Then \(12^{2}+14^{2}=144 + 196=340
eq400 = 20^{2}\).

Answer:

b. Not tangent