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Given that π΅πΆ is a tangent to the circle below, find π β π΄π΅πΆ and π¦Β°.

Given that π΅πΆ is a tangent to the circle, find the measure of angle π΄π΅πΆ and π¦ degrees.

In order to calculate the angle π΄π΅πΆ, we need to use the alternate segment theorem. This states that an angle between a tangent and a cord through the point of contact is equal to the angle in the alternate segment. In our example, this means that angle π΄π΅πΆ is equal to angle π΄π·π΅. This means that angle π΄π΅πΆ is equal to 113 degrees.

In order to calculate π¦, we can use the fact that the inscribed angle, in this case 113 degrees, is half the measure of its intercepted arc. This means that π¦ is equal to 113 degrees multiplied by two. 113 multiplied by two is 226. Therefore, π¦ is equal to 226 degrees.

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