Question

the circle is inscribed in triangle abc. which are congruent line - segments? choose two correct answers. ap and af ab and cb gb and cd fd and gd fp and fd

Explanation:

Step1: Recall tangent - segment property

If two - tangent segments are drawn from an external point to a circle, then the two - tangent segments are congruent.
Let the circle be tangent to \(AB\) at \(E\), to \(BC\) at \(D\), and to \(AC\) at \(F\).
From point \(A\), the tangent segments are \(AE\) and \(AF\). From point \(B\), the tangent segments are \(BE\) and \(BD\). From point \(C\), the tangent segments are \(CD\) and \(CF\).

Answer:

AE and AF, BE and BD, CD and CF are pairs of congruent line - segments. Among the given options, if we assume the correct pairs based on the tangent - segment property, the answer is: AF and AE, BD and BE, CD and CF. But since the options are not in a proper multiple - choice format with letters, we can say that the pairs of congruent line segments are those formed by the tangent segments from the same external point to the circle. If we had to match with the given text in the options: AF and AE would be correct if it was written correctly in the options (similarly for the other pairs based on the tangent - segment rule).