∠BCP = (1/2)arc BC = 69°/2 = 34.5°
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Consider angle BAD. Its measure is 1/2 the measure of arc BD. This remains true no matter where point A may be located on the larger arc BAD. When point A is located on top of point B or D, you have a geometry that is similar to that of angle BCP. The angle measure is still half the arc measure.
