∵pa=pc,sinpba=sinpbc,∴ab/bc=sinapb/sinbpc
AQ/QC of AR/RC = angular bisector theorem
And pq/sin paq = AQ/sin APB, pq/sinpcq = QC/sinbpc of sine theorem.
∴aq*sinpaq/sinapb=qc*sinpcq/sinbpc
That is, AQ/QC=AB/AC*sinPCQ/sinPAQ.
Tangent angle theorem of ∠PCQ=∠QAC, ∠PAQ=∠QCA
∴AQ/QC*sinQCA/sinQAC=AB/AC
Sin qca/sin qac = AQ/QC of sine theorem
∴(AQ/QC)？ =AB/BC
That is, (AR/RC)? =AB/BC
Where is the circular power theorem?