Question

question 13
1 pts
in circle r, line rd is a radius and line df is a tangent. which statement must be true?
○ δ rdf is a right triangle.
○ δ rdf is an obtuse triangle.
○ line rd = line df
○ line rd = line rf

Explanation:

Step1: Recall Tangent-Radius Property

A tangent to a circle is perpendicular to the radius at the point of tangency. So, \( RD \perp DF \), meaning \( \angle RDF = 90^\circ \).

Step2: Analyze Triangle RDF

A triangle with a \( 90^\circ \) angle is a right triangle. So, \( \triangle RDF \) has a right angle at \( D \), making it a right triangle.

• For the other options:
• An obtuse triangle has an angle \( > 90^\circ \), which is false here.
• \( RD \) is a radius, \( DF \) is a tangent segment; there's no reason they are equal.
• \( RD \) and \( RF \): \( RF \) is a hypotenuse (since \( \angle D = 90^\circ \)), so \( RF>RD \), so they aren't equal.

Answer:

A. \( \triangle RDF \) is a right triangle.