(1) Solution: Solving the coordinates of intersection points is equivalent to solving the equation of simultaneous two curves. If the polar coordinates of the intersection point are (l, α), then:

L=2sinα，2 sinα= 2 cosα； ;

Note that (sin α) 2+(cos α) 2 = 1 and α∈[0, π/2];

Solution: α = π/4, L = √ 2;

That is, the coordinate of the intersection point is (√2, π/4).

(2) Solution: From the known:

Angle DAC= angle DBC, angle BDC= angle BAC (the circumferential angles of the same arc in a circle are equal);

Obviously angle EAD+ angle DAC+ angle BAC = 180, angle BDC+ angle DCB+ angle DBC =180;

To sum up, we can get: angle EAD= angle DCB；;

And angle EAD= angle DAC= angle DBC (external angle bisector), that is, angle DBC= angle DCB；;

Therefore, CD=BD=4 (equilateral).