A square and a half square are stacked in order to form a house-shaped quadrilateral. Inside two circles are closely packed. What’s the angle between the tangency points?
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The angle α is 112,5°.
The solution constructs the three angles at tangency point K, leading to α as the rest.
Next the angle OKM is also 90°. This can be seen if you draw the common tangent to L and compare the line segments to the other tangency points. Using the Tangent-tangent theorem, you can show that they are all equal. Hence one can draw a circle and again apply Thales.