Olympiad Geometry Problem #34: IMO Shortlist 2002 G7

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This is such a beautiful and deep problem, only a few lines and you have to prove two circles are tangent, and yet it's very tricky! It's from the 2002 IMO Shortlist. Link below.
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Very nice solution! I'm very impress the way you explained to audience how we can do that.

chetdivedau
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Thank you Micheal this is a great solution. I love it.

OsmanNal
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Please upload theory also because your explanation is very good

AmanKumar-loiz
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Hey brother i am from India, i idea is to show that BNC is 90 so that triangle BNC right angle tri.and by showing that midpoint of BNC is collinear with nd that solve this problem . Am i right

roshnigupta