ZAU CTLR FORGETS TO COORD POINTOUT WHICH CONFLICTS WITH ANOTHER ZAU CTLR'S ACFT.

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I WAS WORKING A SECTOR THAT A PORTION IS ALLOTTED TO ANOTHER SECTOR TO DSND ORD ARRS. DUE TO THIS; ACFT TRANSITING THE DUMP ZONE NEED TO BE POINTED OUT TO THE ARR SECTOR. AN ADJACENT SECTOR PVD'S THE DATA BLOCK OF THE FIRST ACFT SHOWING A CLB TO FL250. AT THAT ALT; I DON'T NEED TO MAKE THE POINTOUT. WHEN THE SECTOR CALLS TO CONFIRM THE POINTOUT; I DECIDE TO STOP THE ACFT AT FL230; SINCE THE ACFT WOULD HAVE TO DSND VERY SOON TO MEET LOA WITH ZOB FOR DET ARRS. I TELL THE ADJACENT SECTOR TO STOP THE ACFT AT FL230 AND CALL RADAR CONTACT. AT THIS ALT; THE ACFT NEEDS TO BE POINTED OUT TO THE ARR SECTOR; BUT AT LEAST THE ORD ARRS WON'T HAVE TO DSND THROUGH THE ACFT; NOR WILL THE ACFT HAVE TO DSND THROUGH THE ORD ARRS. THE SECTOR I AM WORKING IS COMBINED WITH ANOTHER SECTOR AND AT THIS TIME; THINGS COME UP IN THAT AIRSPACE THAT REQUIRE MY ATTN. WHILE ATTENDING TO THESE DUTIES; I AM DISTR FROM THE POINTOUT SIT AND FAIL TO POINT OUT THE ACFT AT FL230 TO THE ARR SECTOR. IN THE SHORT AMOUNT OF TIME I HAD TO ACCOMPLISH THE POINTOUT; NUMEROUS THINGS HAPPENED. MIL ACFT CALLED FOR SUA AND 2 OR 3 XMISSIONS WERE REQUIRED TO CLARIFY WHAT THEY NEEDED. A SECTOR FROM AN ADJACENT CTR CALLED WITH A POINTOUT. 2 OR 3 ACFT CHKED ON FREQ; AND I HAD TO COORDINATE USE OF THE SUA WITH THE SUPVR. ALL THESE WERE COMPLETED; BUT BY THAT TIME; THE ACFT AT FL230 HAD ENTERED THE JOINT USE AIRSPACE WITHOUT A POINTOUT AND I DIDN'T DOUBLECHK TO SEE IF THE POINTOUT WAS DONE OR NOT. I WAS THEN OFFERED A BREAK AND GAVE A BRIEFING TO THE RELIEVING CTLR. AS THAT CTLR TOOK THE SECTOR; I STOOD BEHIND HIM TO MAKE SURE EVERYTHING WAS IN ORDER. THAT'S WHEN THE CONFLICT ALERT WENT OFF BECAUSE THE ARR SECTOR HAD DSNDED AN ACFT THROUGH THE ACFT I DID NOT POINT OUT. IF THE SECTORS WERE NOT COMBINED; THE SIT MAY NOT HAVE OCCURRED. ALSO; THE ARR SECTOR SHOULD OWN THE AIRSPACE.