Angle ACQ = 90°

∴QR is the diameter of circle P, that is, R, P and Q are on the same straight line.

∫∠ADC = 90。

∴EC is also the diameter of circle P.

So point p is on EC.

∴RQ and CE are equally divided

∠∠CQE = 90 degrees.

∴ Quadrilateral RCQE is a rectangle

∴CQ=RE,∠ERC=90

The quadrilateral ABCD is a square.

∴∠RAE=∠DAC=45

△ are is an isosceles right triangle.

∴RE=AE/√2=2√5/√2=√ 10

Namely CQ=RE=√ 10.

When D moves on the extension line of EA, the length of CQ remains unchanged, which is ∴ 10.

I finally succeeded. I wonder if it's too late?