### Video Transcript

Given that π΅πΆ is a tangent to the
circle with center π and the measure of angle π΄ππ· is 97 degrees, find the
measure of angle πΆπ΅π·.

We know that in any circle, a
tangent and radius or tangent and diameter meet at 90 degrees. We are told in the question that
the measure of angle π΄ππ· is 97 degrees. We need to calculate the measure of
the angle πΆπ΅π·. The alternate segment theorem
states that, in any circle, the angle between a chord and a tangent through one of
the endpoints of the chord is equal to the angle in the alternate segment. In this question, the measure of
angle πΆπ΅π· is equal to angle π΅π΄π·.

Letβs now consider how we can
calculate the angle π΅π΄π· using the information on the diagram. Triangle ππ΄π· is isosceles as the
line segment ππ΄ is equal to the line segment ππ·. They are both radii of the
circle. This means that the angles inside
the triangle, angle ππ΄π· and angle ππ·π΄, are equal. These can be calculated by
subtracting 97 from 180 and then dividing by two. 180 minus 97 is equal to 83. Dividing this by two or halving it
gives us 41.5. Angles ππ΄π· and ππ·π΄ are both
equal to 41.5 degrees. As the angle ππ΄π· is the same as
the angle π΅π΄π·, we can see, using the alternate segment theorem, that the measure
of angle πΆπ΅π· is also 41.5 degrees.