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).