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Found problems: 1

2018 Iranian Geometry Olympiad, 4
There are two circles with centers $O_1,O_2$ lie inside of circle $\omega$ and are tangent to it. Chord $AB$ of $\omega$ is tangent to these two circles such that they lie on opposite sides of this chord. Prove that $\angle O_1AO_2 + \angle O_1BO_2 > 90^\circ$. [i]Proposed by Iman Maghsoudi[/i]
geometry geometric ineq angle chasing inequalities