The second shape is not a cyclic quadrilateral. One corner does not touch the circumference. The opposite angles in a cyclic quadrilateral add up to 180°.
When calculating angles using a circle theorem, always state which theorem applies. It may not be possible to calculate the missing angle immediately. It may be necessary to calculate another angle ...
[Henry Segerman] and [Kyle VanDeventer] merge math and mechanics to create a kinetic cyclic scissors sculpture out of 3D printed bars adjoined together with M3 bolts and nuts. The kinetic sculpture ...
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