Even AE, CE, OE, OE in H are handed over to AC.

Due to folding

AO=AE，CO=CE

O is the center of the circle,

So AO=CO

Therefore, AOCE is prismatic. OE vertical AC.

AC=2，

So AH = HC = 1.

pythagorean theorem

r^2= 1/2r^2 + 1^2

r^2 = 2

r = sqrt(2)

Sqrt means root symbol.

2) 40

Explanation:

Mark the position of point D as E before folding.

∠DCA=∠ECA=∠ABE

∠BAE=2*∠BAC=50，∠AEB=90，

Therefore ∠ABE= 180-90-50=40.