first, think about the scenario. You described it yourself, "a car is making a circle on a flat plane." why is it making a circle? you turn the steering wheel to take a left turn, for instance, and your tires move to the left while contacting the road. the reason why they move to the left is because of friction. in a frictionless environment, ie when there's a lot of ice on the ground, you can't turn as well because the friction needed to push the tires is nearly absent.
It all comes down to geometry and vectors.
the key concept is that motion in a circular fashion is different than motion in a straight line.
in a straight line, to accelerate/decelerate, there must be a force in the direction of motion or opposite the direction of motion, respectively. Draw out the vectors.
Think about how changing the velocity is equivalent to acceleration/deceleration (acceleration or deceleration means there is a force acting on the car). Car moving from left to right slows down. before the deceleration the velocity vector is pointing to the right. As the car slows down, the velocity vector pointing to the right gets smaller in length. see below diagram:
initial velocity vector: ----->
final velocity vector (choose this to be some point when the car is slowing down): --->
velocity vector at some point of deceleration:
change in velocity = final velocity - initial velocity, in vector terms you need to add the final velocity vector arrow to the initial velocity vector arrow pointing in the opposite direction like this:
change in velocity = ---> + <----- = <-- (this is the direction of the applied force!)
in a circle, the car's velocity vector is tangent to the circle.
Sorry this was kind of long winded, but if you still don't understand let me know! hope this helps
