Thales' Triangle

Geometry Level 3

Given a triangle \(ABC\), consider the bisector of \(\measuredangle A\) which intersects \(BC\) at the point \(D\).

If \(CD + AC = 12\text{ cm}\) and \(CD = \dfrac{BC}{3}\), What is the perimeter of the triangle (in \(\text{cm}\))?

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