## National Camp 2013 Geomretry Prb 2

Discussion on Bangladesh National Math Camp
asif e elahi
Posts: 183
Joined: Mon Aug 05, 2013 12:36 pm

### National Camp 2013 Geomretry Prb 2

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\$ .

Kazi_Zareer
Posts: 86
Joined: Thu Aug 20, 2015 7:11 pm
Location: Malibagh,Dhaka-1217

### Re: National Camp 2013 Geomretry Prb 2

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.