According to the given examples, identify the case where a balanced force acts on it.

When more than two forces act on a body and all of the forces balance each other, the resultant force acting on the object is zero, and the object is said to be at equilibrium.

The object must be at rest or in uniform motion with constant velocity if the forces acting on it are balanced. 

As the person is at rest, "A person resting on an armchair" is the best choice. 

There is an unbalanced force acting on it in the other options. 

• "A cyclist braking" has a negative force acting against the cycle, causing it to stop, and 
• "A car that has a deceleration of $10 \mathrm{m}/{\mathrm{s}}^2$" has the object coming to a stop, but it is not at rest, so the force acting cannot be said to be balanced.