The circular motion of a particle with constant speed is:
1) Periodic but not SHM
2) SHM but not periodic
3) Periodic and SHM
4) Neither periodic nor SHM

Hint: Any motion which repeats itself after a regular interval of time is defined as periodic.
When an object is in motion which observes oscillations have simple harmonic motion.
Using the above hint to the type of motion mentioned in the question we identify the type of motion a particle is having in circular motion.

Complete step by step solution:
Let’s define periodic motion and simple harmonic motion in a more elaborated manner:
The motion of an object or a body which is regular and repeating is referred to as periodic motion. There are many vibrating objects which repeat their motion after every interval in the same phase .When a spring is taken and is hanged on a hook .The hanging end of the spring is attached to some mass which produces motion in the spring and it keeps on repeating after regular intervals.
Simple harmonic motion: motion which has oscillations present in it is with restoring force is called simple harmonic motion. Simple harmonic motion can be well understood by the example of pendulum. Pendulum once made to move repeats its motion to and fro with oscillations along the restoring force acts along the centre of the pendulum.
When a particle moves in a circular motion, its motion is periodic because after completing one revolution a particle again comes back to the same position but no oscillations with no restoring force is present in the motion which means that the motion is periodic but not simple harmonic.

Option 1 is correct.

Note:Periodic motion is also seen in a sinusoidal wave which repeats itself after a regular interval. We also relate our current and voltage phasors, in terms of sinusoidal waves and thus the output of power we obtain is also a sinusoidal wave with some harmonics (dc component) in it.