First of all, when at first the question file of was uploaded, there was a little flaw in question (short) , and so we uploaded the new file with an addition in the question (length of AC)
But later, when the results were out and solution file was uploaded, the solution was as per the previous (wrong) version of the question, so results will be posted once again.
To put a fullstop to all the disputes and clarifications, I am writing this note.
Question (JOMO 7, short 9) :- In , is the incenter, and meet the sides at points respectively. . Then the ratio can be written as where and are coprime positive integers, find
We will use the angle bisector property in ,
Thus we have
Now, we use angle bisector property for ,
Thus we get
Now, (length of the angle bisector)
So we get the value of
Similarly, we get
Then , after taking their ratio, answer comes as
And, finally, putting values
And when you put , answer is , hence the asked value is .