October 26th, 2009, 01:08 PM  #1 
Newbie Joined: Oct 2009 Posts: 4 Thanks: 0  Geometry  triangle
A triangle ABC, which has is inscribed into circle with centre S. Line CS intersects segment AB in point D. Show that if then radii of incircles of ADC and BDC have the same length.

October 26th, 2009, 02:56 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,852 Thanks: 1570 
The above is problem 7 from the first round of the current Polish National Olympiad, being held in September to November this year. Another problem you posted is problem 6 from the same source. It is reasonable to assume you submit your own work for these problems in order to qualify for the next round. I therefore ask people here not to offer help on these questions until December 2009.

October 26th, 2009, 03:02 PM  #3 
Senior Member Joined: Mar 2007 Posts: 428 Thanks: 0  Re: Geometry  triangle
I have other thoughts as to why such problems are posted and posted here rather than in some other more suitable forums I've attended, but will let that pass. I'd simply add the same old suggestion: Don't do anything for anyone who shows nothing for themselves. That is, unless you are spending time in jail and need something to pass the time.

October 26th, 2009, 08:31 PM  #4 
Senior Member Joined: Oct 2009 Posts: 105 Thanks: 0  Re: Geometry  triangle
Nice catch skipjack. I've never heard of the Polish National Olympiad. *looks it up* 

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