Hello, ineedhelp!

You are in the center of a circle of radius R.

Some angry dog runs exactly along the circumference of the circle and tries to bite you.

The dog can run 4 times faster than you.

Devise a strategy that will let you run away from the circle unharmed.

Run toward the point diametrically opposite the dog. Code:

Dog
* o *
* *
* *
* *
* You *
* o *
* ↓ *
* *
* *
* *
* * *

He will commit himself by choosing a direction around the circle.

Let's say he runs clockwise.

Curve your path so the center of the circle

. . is always between you and the dog. Code:

* * *
* *
* o
* / *
/
* / *
* * *
* / + *
+ +
* *
* *
* *
* * *

You will spiral outward and reach the perimeter

. . and the dog will still be diametrically opposite.

Code:

* * *
* *
+ *
*+ \ *
\
* + \ *
* * *
* + + \ *
+ + \
* \ *
* o
* *
* * *

I hope your car is close enough for you to sprint to it.