AWK and print next lines #3 thru #10

I have a output log file, that I want to extract some temperature measurement data.

I want to AWK on the words "show chassis environment" in the original file, and extract that entire line, and then the 3rd to 10th lines after the one I AWK'd, into a seperate output file.

Here is an example of the information in the source file :

20:52:34_23C | root@HWTestEng-Gext% 
20:52:35_23C | 
20:52:35_23C | root@HWTestEng-Gext% cli show chassis environment
20:52:35_23C | 
20:52:35_23C | Class Item                           Status     Measurement
20:52:36_23C |       PCB Left                       OK         33 degrees C / 91 degrees F
20:52:36_23C |       SFP+ Xcvr                      OK         33 degrees C / 91 degrees F
20:52:36_23C |       FEB                            OK         50 degrees C / 122 degrees F
20:52:36_23C |       PCB Up                         OK         33 degrees C / 91 degrees F
20:52:36_23C |       PCB Mid                        OK         36 degrees C / 96 degrees F
20:52:36_23C |       Telecom Mod                    OK         37 degrees C / 98 degrees F
20:52:36_23C |       Routing Engine                 OK         31 degrees C / 87 degrees F
20:52:36_23C |       Heater off                    
20:52:36_23C | root@HWTestEng-Gext% 

the information I want to extract and export to another file would be:

20:52:35_23C | root@HWTestEng-Fortius-Gext% cli show chassis environment
 20:52:36_23C |       PCB Left                       OK         33 degrees C / 91 degrees F
20:52:36_23C |       SFP+ Xcvr                      OK         33 degrees C / 91 degrees F
20:52:36_23C |       FEB                            OK         50 degrees C / 122 degrees F
20:52:36_23C |       PCB Up                         OK         33 degrees C / 91 degrees F
20:52:36_23C |       PCB Mid                        OK         36 degrees C / 96 degrees F
20:52:36_23C |       Telecom Mod                    OK         37 degrees C / 98 degrees F
20:52:36_23C |       Routing Engine                 OK         31 degrees C / 87 degrees F
20:52:36_23C |       Heater off

Does this work for you?
(And yes, I know I can get rid of that useless 'cat'!!)

$ cat sample1.txt | grep "show chassis" -A10 | grep -e "degrees" -e "chassis"
20:52:35_23C | root@HWTestEng-Gext% cli show chassis environment
20:52:36_23C |       PCB Left                       OK         33 degrees C / 91 degrees F
20:52:36_23C |       SFP+ Xcvr                      OK         33 degrees C / 91 degrees F
20:52:36_23C |       FEB                            OK         50 degrees C / 122 degrees F
20:52:36_23C |       PCB Up                         OK         33 degrees C / 91 degrees F
20:52:36_23C |       PCB Mid                        OK         36 degrees C / 96 degrees F
20:52:36_23C |       Telecom Mod                    OK         37 degrees C / 98 degrees F
20:52:36_23C |       Routing Engine                 OK         31 degrees C / 87 degrees F

YES - That Works !!! Thanks !

AWK:

awk '/show chassis environment/&&p=1;p&&p++>3&&p<13' file