(CNN) -- As the Olympic flame burned above Sochi on Tuesday evening, a scene of mayhem and death exploded a few hundred miles away in the Ukrainian capital, Kiev, where blazes roared and violent clashes erupted along protesters' barricades. At least 100 people were killed just on Thursday and hundreds more hospitalized in confrontations pitting government forces against demonstrators opposed to a regime that has strong support from President Vladimir Putin's Russia. It was the deadliest day in the three months since the showdown started. Between the two spectacles, you can bet Putin's attention focused more sharply on the crisis in Ukraine, which is officially an independent country since 1991 but in reality remains a state over which Moscow exercises enormous influence, infuriating much of Ukraine's population.
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Frida Ghitis: New Russia on display in Sochi, but the old one is showing its face in Ukraine
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Ghitis: Putin has called Ukraine "Little Russia" and wants it to turn away from the West
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Ghitis: Protesters enraged by seeing their leaders' knuckle under Russia's bullying
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As demonstrators refuse to stop, she says, Putin should be worried they might prevail
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