MHB How to Cook the Perfect Steak"Cook Perfect Steak: Step-by-Step Guide

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The discussion focuses on the geometric relationship between arc BC and angle BAC, highlighting that their measures are equal. It emphasizes the role of the perpendicular bisector, which bisects segment BC and intersects line AD at the circle. This intersection implies that the bisector also divides arc BC into two equal parts. Participants seek a more formal way to articulate these geometric principles. The conversation centers around understanding and expressing these relationships in a precise manner.
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Do you see that the measure of arc BC is the same as the measure of angle BAC?
 
Country Boy said:
Do you see that the measure of arc BC is the same as the measure of angle BAC?
Ohhh, and then because the perpendicular bisector bisects BC and meets AD at the circle, it must cut the arc in half? Is there a more formal war to write that?
 
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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