Two circles touch internally at A. The tangent at P on the smaller circle cuts the larger circle at Q and R. Prove that AP bisects angle RAQ.
Pleas help?
This one can also be done with the help of Alternate segment theorem
Let AR intersect smaller circle at N
Let AQ intersect smaller circle at M
Join MN
Draw a tangent a A
Let Y be the point on tangent such that angle RAY is acute
Let Z be the point on tangent such that angle RAY is obtuse
The following relation follows from Alternate Segment theorem
RAY=RQA
PAY=PMA
QAZ=QRA
PAZ=PNA
PAQ=PAZ-QAZ
=PNA-QRA
=RPN
=PAR(Alternate ST,smaller circle, tangent at P, chord PN)
Hence, proved.