### Video Transcript

Find the measure of angle
π΅π΄πΆ.

Letβs begin by marking the angle
whose measure weβve been asked to find on the diagram.

We can now see that weβve been
asked to calculate an angle of tangency, because the marked angle is the angle
between the tangent π΄πΆ and the chord π΄π΅. We can therefore recall the
following theorem. The measure of an angle of tangency
is equal to half the measure of the central angle subtended by the same arc. The arc that connects the endpoints
of the chord π΄π΅ is the minor arc π΄π΅, and the central angle subtended by this arc
is angle π΄ππ΅.

So we have that the measure of
angle π΅π΄πΆ is half the measure of the angle π΄ππ΅. The angle π΄ππ΅ is marked on the
diagram with a small square, indicating that it is a right angle. So its measure is 90 degrees. The measure of angle π΅π΄πΆ is
therefore equal to one-half of 90 degrees, which is 45 degrees.

So, by identifying that angle
π΅π΄πΆ is an angle of tangency and then recalling that the measure of an angle of
tangency is half the measure of the central angle subtended by the same arc, weβve
found that the measure of angle π΅π΄πΆ is 45 degrees.