How can we find the magnitude of centripetal acceleration?
Consider an object moving at a constant speed around a circle. We observe it twice.

Each line is a radius, and each represents one observation time.
The two black lines are radii, and represent the two observations of the moving object.
The blue line is the difference between the two radii.
Dr = r2 - r1
The red lines are the velocity vectors.  They point at 90° from their radius.  Remember, if you swing a rock on a string and release it, it flies at a right angle to the last string direction.
The green line is the difference between the two velocity vectors.  The bottom velocity vector "v1" was slid upward along the dotted line so we could see the triangle.
Why do all this?
We needed to recognize that the angles made by these vectors are equal.  This means that the two triangles (radii & velocity) are similar.
For the radii, sinq = Dr/r
For the velocities, sinq = Dv/v
Setting these two equal to each other, we can arrive at Dv = Dr*v / r

If we divide both sides by Dt, we get Dv/Dt = Dr*v / rDt

Notice that we have Dv/Dt, this is our old equation for acceleration!
ac = Dr*v / rDt

Notice that we have Dr/Dt, which is a way of giving velocity along a circle!
ac = v*v / r = v2/r
This is the equation for finding centripetal acceleration.  This particular version will give an answer in m/s/s.