# Question Video: Finding the Measure of an Angle of Tangency Given the Measure of the Central Angle Subtended by the Same Arc Mathematics • 11th Grade

Find πβ π΅π΄πΆ.

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### Video Transcript

Find the measure of angle π΅π΄πΆ.

Letβs begin by marking the angle whose measure weβve been asked to find on the diagram.

We can now see that weβve been asked to calculate an angle of tangency, because the marked angle is the angle between the tangent π΄πΆ 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΄ππ΅.

So we have that the measure of angle π΅π΄πΆ is half the measure of the angle π΄ππ΅. The angle π΄ππ΅ 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΄πΆ is therefore equal to one-half of 90 degrees, which is 45 degrees.

So, by identifying that angle π΅π΄πΆ 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, weβve found that the measure of angle π΅π΄πΆ is 45 degrees.