Geometry Problem 1611: Angle Calculation in Triangle ABC with Auxiliary Construction

Geometric diagram of triangle ABC with angles 34 and 107 degrees, showing point D on the internal angle bisector of A such that CD equals BC for calculating angle ACD
$$ \begin{array}{l} \textbf{GIVEN:}\\ \triangle ABC, \angle A = 34^\circ, \angle B = 107^\circ \\ D \text{ is on the bisector of } \angle A \\ \text{ such that } CD = BC \\ \\ \textbf{FIND:}\\ m\angle ACD \end{array} $$
Diagram: Triangle ABC with bisector and equidistant point D.

Problem Statement

In a triangle \( ABC \), the measures of the interior angles at \( A \) and \( B \) are \( 34^\circ \) and \( 107^\circ \), respectively. Let \( D \) be a point on the internal bisector of \( \angle BAC \) such that the segment lengths \( CD \) and \( BC \) are equal.

Determine the measure of the angle \( ACD \).

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