I seem to have stumbled on a formula for generating some geometry problems.
(i) Combine two familiar shapes to create a composite irregular polygon.
(ii) Fit one or two circles inside the construction.
(iii) Adjust the shapes to fit precisely.
In this problem a quadrilateral is composed of a 30-60-90° triangle abutting a 45-90-45° triangle, long side to short side. A circle is fitted that is tangential to two sides of the 45-90-45° triangle and to the short side of 30-60-90° triangle. What is the radius of the circle? Scale the diagram as convenient for your calculations. This is the first of a series of four problems.
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