Question -
Answer -
In the given problem, BP and CP arethe internal bisectors of 
respectively. Also, BQ and CQ arethe external bisectors of respectively. Here, we need toprove:
We know that if the bisectors of angles
and 
of ΔABC meetat a point O then
Thus, in ΔABC
……(1)
Also, using the theorem, “if the sides AB and AC of a ΔABC are produced, and theexternal bisectors of 
and 
meet at O, then 
Thus, ΔABC
∠BQC=90°−12∠A ......(2)∠BQC=90°-12∠A ......2
Adding (1) and (2), we get
Thus, 
Hence proved.