MHB Inscribed Angles to Identifying and Understanding

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Identifying inscribed angles can be challenging, even with knowledge of the relevant theorem. A suggested method involves sketching lines from the center of the circle to the points where the inscribed figure intersects the circle. This visual representation may clarify the relationships between the angles and the arcs they subtend. Understanding how these angles relate to the circle's geometry is essential for accurate identification. Applying these techniques can enhance comprehension of inscribed angles.
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I've been having trouble identifying these inscribed angles for a while. I know the theorem that goes with this topic but I'm unsure how it applies :c.
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Sketch lines out from the centre of the circle to where the points of the inscribed figure meet the circle. Does that help?
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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