Find bounding box coordinates for a geometric shape - json

Question

I have a JSON file that contains the geometric information about the sketch. The file is in the following format:
"Name": Name of the geometric entity
"Type": Type of the entity, either a line or an arc (a circle is represented by an arc and a rectangle as a set of 4 such dictionaries of type line.)
If the entity is of the type line, then the dict would contain the coordinates of the starting and ending points of the line.
If it is of the type arc, then the dict would contain the radius, the coordinates of the center and the starting and ending points of the arc.
Here is an example of each type:
Type == Line
"Name": "Line8",
"Type": "Line",
"Start Point": [
0.0,
-13.694950218796503,
127.7623417068559
],
"End Point": [
0.0,
-12.800696621739458,
121.82935674950514
],
"Length": 5.999999999999998
Type == Arc
"Name": "Arc4",
"Type": "Arc",
"CentrePoint": [
0.0,
0.0,
0.0
],
"Radius": 137.0,
"RotationAngle": 0.0,
"StartAngle": 1.5474413367198918,
"EndAngle": 1.5941513168699013,
"Circumference": 6.399267280551308
A JSON file will contain multiple such dictionaries for multiple geometric entities that make up a geometric sketch.
I want to create a bounding box around that sketch and need its coordinates.
My initial approach was to just take the min and max values of the x, y and z coordinates from these dictionaries to define a bounding box. But by doing this I might end up missing the curves in the arcs since I only have information about the center of the arc and not the points on the arc.
How should I go about getting the bounding box coordinates given this JSON file?