Question

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

Explanation:

Step1: Recall the Pythagorean theorem

If a line is tangent to a circle, then the radius is perpendicular to the tangent at the point of tangency, and the triangle formed by the radius, the tangent - segment, and the line from the center of the circle to the end - point of the tangent is a right - triangle. Let the radius of the circle be $r = 7$ (since the diameter is 14, $r=\frac{14}{2}=7$), the length of the segment from the external point $B$ to the point of tangency $A$ be $a = 12$, and the length of the line from the center of the circle to the external point $B$ be $c = 20$.

Step2: Apply the Pythagorean theorem

In a right - triangle, $a^{2}+r^{2}=c^{2}$ if the triangle is a right - triangle. Calculate $a^{2}+r^{2}$: $12^{2}+7^{2}=144 + 49=193$. Calculate $c^{2}$: $20^{2}=400$. Since $12^{2}+7^{2}
eq20^{2}$, the triangle is not a right - triangle.

Answer:

b. Not tangent