This sentence is wrong, right? Is it along the x axis?

When (1)t=0, O and A coincide, so D (0,4).

② Because AC=BC, CD⊥AB.

So d is the midpoint of AB.

In the right triangle AOB,

The center line of the hypotenuse is equal to half of the hypotenuse.

So OD=AB/2=4.

(3) A circle with C as the center and AC as the radius is tangent to the X axis.

That is, when AC is perpendicular to the x axis.

It can be proved that the triangle ACD is similar to the triangle BAO.

So AC/BA=CD/AO.

5/8=3/AO

AO=24/5

So t=24/5