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USAMO 1987 Problem 2

The feet of the angle bisectors of the triangle ABC\mathrm{ABC} form a right-angled triangle. If the right-angle is at X\mathrm{X}, where AX\mathrm{AX} is the bisector of angle A\mathrm{A}, find all possible values for angle A\mathrm{A}.

Dataset text NuminaMath olympiads. Quoted with source.

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120^{\circ}

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