Question

the circle is inscribed in triangle aec. which are congruent line segments? select two options.
ab and cb
ef and ed
ed and cd
af and ef
cb and cd

Explanation:

Step1: Recall the tangent - segment theorem

If two tangent segments are drawn from the same external point to a circle, then the two tangent segments are congruent.

Step2: Analyze each option

• For \(\overline{EF}\) and \(\overline{ED}\):

Since \(E\) is an external point and \(EF\) and \(ED\) are tangent segments to the circle, by the tangent - segment theorem, \(\overline{EF}\cong\overline{ED}\).

• For \(\overline{CB}\) and \(\overline{CD}\):

Since \(C\) is an external point and \(CB\) and \(CD\) are tangent segments to the circle, by the tangent - segment theorem, \(\overline{CB}\cong\overline{CD}\).

Answer:

\(\overline{EF}\) and \(\overline{ED}\), \(\overline{CB}\) and \(\overline{CD}\)