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Answer :
The measure of ">∠BPC" is 108°, found by using the property of circles that states the angle between a tangent and a chord is equal to the angle in the alternate segment. Therefore, the correct answer is option B.
To solve this, we can use properties of a circle and its tangents. According to the properties, angle formed between a tangent and a chord through the point of contact is equal to the angle subtended by the chord in the alternate segment.
Since ">∠BAC" is 54°, this means ">∠BPC" will be twice as much because it is an exterior angle to triangle ABC formed by extending line AC to point P. Therefore, ">∠BPC" = 2 imes 54° = 108°. Therefore, the correct answer is option B.
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