Geometry · Isosceles triangles · Angle chasing · Right triangles · Contact triangle
In triangle \(ABC\) the angle at \(A\) is a right angle. Points \(D\), \(E\) and \(F\) are chosen on the sides \(AB\), \(BC\) and \(CA\) respectively, so that
\[ |BD| = |BE| \qquad\text{and}\qquad |CF| = |CE| , \]
as in the figure. How many degrees does the angle \(\angle FED\) measure?
- A \(30\)
- B \(37.5\)
- C \(45\)
- D \(52.5\)
- E It cannot be determined, because the answer depends on the size of \(\angle CBA\).
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2023, 1. letnik, category A, problem A2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source