National Camp 2013 Geomretry Prb 2

Discussion on Bangladesh National Math Camp
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asif e elahi
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Location: Sylhet,Bangladesh

National Camp 2013 Geomretry Prb 2

Unread post by asif e elahi » Thu Jan 30, 2014 10:55 pm

The incircle of triangle $ABC$ touches $BC,CA,AB$ at $D,E,F$ respectively . The circle passing through $A$ and touching the line $BC$ at $D$ intersects $BF$ and $CE$ at points $K$ and $L$ respectively . The line passing through $E$ and parallel to $DL$ and the line passing through $F$ and parallel to $DK$ intersects at $P$ .
Let $R_1,R_2,R_3,R_4$ be circumradius of $\Delta AFD, \Delta AED , \Delta FPD , \Delta EPD $ . Find the value of $k$ for which $R_1R_4=k . R_2R_3$ .

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Kazi_Zareer
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Location: Malibagh,Dhaka-1217

Re: National Camp 2013 Geomretry Prb 2

Unread post by Kazi_Zareer » Sat Feb 04, 2017 12:48 pm

https://artofproblemsolving.com/communi ... 84p2641339
$k = 1 $
The original source of this problem was: Turkish TST 2012 Problem 4
We cannot solve our problems with the same thinking we used when we create them.

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