Let's evaluate the given statement:
The measure of a tangent-tangent angle is twice the difference of the measures of the intercepted arcs.
To understand this, let's break down the key concepts:
1. Tangent-Tangent Angle: When two tangents intersect outside a circle, they form an angle known as the tangent-tangent angle.
2. Intercepted Arcs: When these tangents touch the circle, they "intercept" two arcs on the circle. One is the minor arc (smaller arc), and the other is the major arc (larger arc).
The measure of the tangent-tangent angle is related to these intercepted arcs. The actual relationship is given by:
[tex]\[ \text{Measure of the tangent-tangent angle} = \frac{1}{2} \times (\text{Major Arc} - \text{Minor Arc}) \][/tex]
The correct formula states that the measure of the tangent-tangent angle is half the difference of the measures of the intercepted arcs, not twice the difference.
So, translating the original statement into this context:
The measure of a tangent-tangent angle is twice the difference of the measures of the intercepted arcs.
This statement is false because it incorrectly states that the angle is twice the difference, whereas it should be half the difference.
Therefore, the correct answer is:
B. False
