The Book of Lemmas: Proposition 8
If CD is any chord of a circle whose center is O, and if CD is extended to A so that AD is equal to the radius; if further AO is extended to meet the circle in B, then the angle BOC will be equal to three times the angle BAC.
Click on the plot below to add points C and D to the circle, and there create the chord CD. Then, click "Extend CD to point A" to extend this chord to the point A. Finally, click "Compare angles BAC and BOC" to view these angles on the plot and observe their angle measurements. Notice that angle BOC is always equivalent to three times angle BAC.
Measure the angles in
Angle BAC =
Angle BOC =
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