BP=PC ,CQ=DQ, AP and AQ bisects angle BAC and CAD respectively.Prove that:1)∆ABD is an isosceles ∆.2)PQ//BDRefer to the question attached in the image.

Dear Student
Triangle ABC is isosceles because BP=PC and AP is angular bisector , so AB=AC
Similarly Triangle ADC is isosceles because AD=AC. so AB=AD therefore ABD is isosceles
Trinagle BDC is similar to triangle PQC by similarity criterion.

So BD and PQ are inclined at same angle