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Geometry · Incenter · Angle bisectors · Isosceles triangles

Problem 3, 2005

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NationalOpen answer

Let \(I\) be the incenter of a triangle \(ABC\), and suppose that

\[ |CA| + |AI| = |BC| . \]

Determine the ratio of the sizes of the angles \(\angle BAC\) and \(\angle CBA\).

A B C I
The incenter \(I\) of triangle \(ABC\). The hypothesis links the two sides drawn from \(A\) and \(C\): \(|CA| + |AI| = |BC|\).

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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2005, 1. letnik, category A, problem 3. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source

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