The proof idea is as follows:

There are two ways to prove the connectivity of OC: QA=QC.

Method 1: Because OE is both the bisector of the angle AOC and the height of the AC side, the triangle OAC is an isosceles triangle.

And OE is also the center line of AC side.

In the triangle QAC, QE is both the height and the middle line of the AC side, so the triangle QAC is an isosceles triangle with AC as the base.

So, QA=QC

Method 2: Using triangle congruence, QA=QC can also be proved.

Therefore, QA+PQ=CQ+PQ.

If and only if the straight lines C, Q, P*** are the height of the OAC OA side of the triangle, QA+PQ=CQ+PQ is the minimum. From the area and the length of OA, we can know that the height of OA side is 3.

Therefore, the minimum value of AQ+PQ is 3.