Question

which of the lines or segments below is tangent to circle o?
answer
\\( \overline { j b } \\)
\\( \overleftrightarrow { j f } \\)
\\( \overline { b c } \\)
\\( \overleftrightarrow { g a } \\)

Explanation:

Step1: Recall the definition of a tangent

A tangent to a circle is a line that touches the circle at exactly one point.

Step2: Analyze each option

• $\overline{JB}$: This is a chord (a line segment with both endpoints on the circle), not a tangent.
• $\overleftrightarrow{JF}$: This line intersects the circle \(O\) at two points (\(B\) is on circle \(O\) and \(C\) is on the other circle, but considering circle \(O\), it has two - point intersection with circle \(O\) if we consider the extension, so it's a secant (a line that intersects a circle at two points), not a tangent.
• $\overline{BC}$: This is a line segment that is part of a secant (since the line containing \(BC\) intersects circle \(O\) at \(B\) and the line \(\overleftrightarrow{JF}\) which is related to circle \(O\)'s intersection).
• $\overleftrightarrow{GA}$: This line touches circle \(O\) at exactly one point \(G\). By the definition of a tangent (a line that touches a circle at exactly one point), \(\overleftrightarrow{GA}\) is tangent to circle \(O\).

Answer:

\(\overleftrightarrow{GA}\)