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Part of 1968 German National Olympiad

Problems(1)

isosceles iff 2 equal angle bisectors: Germany 1998 R3 9.3. 1968 Ρ4 12.6

Source:

Prove the following two statements: (a) If a triangle is isosceles, then two of its bisectors are of equal length. (b) If two angle bisectors in a triangle are of equal length, then it is isosceles.

geometryangle bisectorisosceles