Problem: Construct the cyclic quadrangle from the lengths a, b, c, d of its sides.
Rotate triangle (ACD) about C to the position (ECF). [FE] is parallel to [BG] and the length BG can be constructed from (BG/BC) = (FE/FC) = (AD/DC). Then point C is found as intersection of the circle (B, BC) and the Apollonian circle on (AG) for the ratio k = (CA/CG) = (CE/CG) = (CF/CB) = (CD/CB). Knowing the positions of A, B, C the construction of the circle and of D is easy.
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Cyclic quadrangle construction ![[0_0]](Inscriptible_Construction_files/Inscriptible_Construction_0_0_0.png)
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