In triangle ABC on the side AC point D is chosen so that BC=BD. On the side AB selected points P and Q so that ∠PDA=∠QCA=∠BAC. Need to prove that AP=BQ.
I have the following idea. Note that the triangles APD and AQC are isosceles. Then AP=PD and AQ=QC. Next apply the Intercept theorem, we obtain
APAD=PQDC.
I'm stuck at this step. In what direction you need to continue to argue?
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