Really bad plat
How many corners have you found?
We have plenty of old recorded plats similar to the example shown. Although one can (at times) calculate circular curves on these plats that fit the dimensional criteria given, I'm not so sure some of them were ever actually meant to be circular curves. I have seen a few plats that were most likely drawn with a French curve (an antique drafting tool).
Surveying within these plats can teach a surveyor a lot about understanding what was actually being shown on the document or implied by the document and what wasn't. Assuming there is mathematical harmony and logic within some plats may just be wishful thinking.
That is a bad plat. Reminds me of a local subdivision that was created by an engineer that worked heavily on railroad projects a long time ago. As you can guess, all of the curves were railroad curves. Total pain assured for anyone who didn't know the engineer's history.
In the late 80's I worked for an Engineer/Surveyor that had done many subdivisions just like that in the late 60's and early 70's. The party chief/old timer that did the fieldwork was still there and still the party chief. Those subdivisions were designed on the ground and surveyed enough to make a plat in the office. There was no design and go stake it out. Any distance that was not measured on the ground was scaled between the dots on paper.
That 150 foot is the length of the arc and may have been measured with a cloth tape sorta draped around the arc where they wanted the line. Forget math, there was none.
Check the deeds. There are plats of this type recorded in the Portland area. Sometimes the lots are described by M&B in the deeds, thus filling in missing information.