Question

in circle r, \\(\overline{rd}\\) is a radius and \\(\overline{df}\\) is a tangent segment. which statement must be true? \\(\circ\\) \\(rd = rf\\) \\(\circ\\) \\(\triangle rdf\\) is an obtuse triangle. \\(\circ\\) \\(\triangle rdf\\) is a right triangle. \\(\circ\\) \\(rd = df\\)

Explanation:

Step1: Recall tangent-radius property

A tangent to a circle is perpendicular to the radius at the point of contact. Here, $\overline{DF}$ is tangent at $D$, so $\overline{RD} \perp \overline{DF}$.

Step2: Analyze triangle RDF

Since $\angle RDF = 90^\circ$, $\triangle RDF$ has a right angle.

Answer:

$\triangle RDF$ is a right triangle.