Show that $\angle {ABC }$ is bisected by line OC

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Here is the construction

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Show that $\angle {ABC }$ is bisected by line OC, Got any ideas?

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In step iii, you are asked to construct a circle that literally touches all three line segments that form the triangle (without extending the sides of the triangle). Spoiler alert for step iv: this is called the incircle of a triangle. See this link for more details, but in general it should look like: enter image description here