Let's begin with constructing a circle centered at point P using the compass.
Next we will draw a chord. To do this we will choose two points that lie on the circle and connect them with a segment. Let's call the points A and B.
Now we will measure the chord using a ruler.
To measure the distance that the chord is from the center we should draw a radius of ∘ P that is a perpendicular bisector of AB. Let's name the point of intersection of this radius and AB as X.
The distance that the chord is from the center is PX. Let's measure this length using the ruler.
To find the length of the radius, PA, notice that △ APX is a right triangle.
Therefore we can find PA using the Pythagorean Theorem. According to this theorem, the sum of the squared legs of a right triangle is equal to its squared hypotenuse.
PA^2=AX^2+PX^2
Let's substitute the appropriate values into the above equation. Notice that since PA represents a length we will consider only the positive case when taking the square root of PA^2.
