OP (original poster) is Occiput Posterior and OA is Occiput Anterior. OP (original poster) means the baby is sunny side up and OA means baby is face down. Left OA is the preferred birthing position for the baby.

Introduction:
In order to understand why OA = OP, we need to understand the concept of a chord and its properties in a circle.

Definition of a Chord:
A chord is a line segment that connects any two points on the circumference of a circle.

Property of a Chord:
The perpendicular bisector of a chord passes through the center of the circle.

Explanation:
Now, let's consider a circle with center O and a chord AB.

Step 1: Drawing Perpendicular Bisectors:
Draw the perpendicular bisectors of the chord AB. Let's call the point where the bisectors intersect as point P.

Step 2: Identifying Key Points:
Let's label the midpoint of chord AB as point M. We know that the perpendicular bisectors of a chord pass through the center of the circle. Therefore, point P lies on the line OM.

Step 3: Establishing Congruence:
Since P is the midpoint of chord AB and M is the midpoint of chord AB, we can conclude that PM is the perpendicular bisector of chord AB. This implies that PM passes through the center of the circle (point O).

Step 4: Understanding Congruence of Triangles:
Now, let's consider the right-angled triangle OPA.

- Side OA is the radius of the circle.
- Side OP is the length of the segment PM.
- Angle OPA is a right angle.

Since PM is the perpendicular bisector of chord AB, it is also perpendicular to the radius OA. Therefore, angle OPA is a right angle.

Step 5: Applying Pythagoras Theorem:
According to the Pythagoras theorem, in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In triangle OPA, we have:
OP^2 = OA^2 + PA^2

However, since PA is the other half of chord AB and is equal to OA, we can substitute PA with OA:
OP^2 = OA^2 + OA^2

Simplifying the equation, we get:
OP^2 = 2OA^2

Taking the square root of both sides, we find:
OP = √2 * OA

Therefore, we can conclude that OA is equal to OP.

Conclusion:
In a circle, the length of the radius (OA) is equal to the distance between the center of the circle (O) and any point on the circumference of the circle (P). This can be proved using the concept of perpendicular bisectors and the Pythagoras theorem.