### Video Transcript

Given that line segment π΄π΅ and line segment π΄πΆ are two tangents to the circle π and the measure of the angles ππ΄πΆ is equal to 21 degrees, determine the measure of angle πΆπ΄π΅.

Letβs simply begin by looking at what we do know about our diagram. We have a circle with two tangents π΄π΅ and π΄πΆ. We can see that the point π must be the center of the circle. And that means the lines π΅π and πΆπ must be the radii of the circle. So what does it mean for triangles π΄π΅π and π΄πΆπ?

Well, we know by definition that the radii must be of equal length. So the length of the line π΅π must be equal to the length of the line πΆπ. We also know that a tangent and a radius meet at 90 degrees. So the measure of angle π΄π΅π must be equal to the measure of angle π΄πΆπ, which is equal to 90 degrees. We know that tangents from the same point are equal in length. So lines π΄π΅ and π΄πΆ must be equal. But thereβs also a shared line here. The line π΄π is common to both triangles.

So now, we have two triangles which both have a right angle. They have a hypotenuse which is shared and they have two other equal sides. So we can pick and choose which condition for congruency we wish to quote. We could choose SSS. All three sides are equal in the triangles. So the two triangles must be congruent. We could choose RHS. The triangles have a right angle, an equal hypotenuse, and one other side of equal length. It doesnβt really matter which condition we choose though. Whatβs important is that we have identified that the triangles are congruent.

This means we can now assume the other angles must be equal. And therefore, angle ππ΄π΅ must be equal to angle ππ΄πΆ, which we were told was 21 degrees. So the measure of angle πΆπ΄π΅ must be equal to 21 plus 21, which is equal to 42. And the measure of angle πΆπ΄π΅ is 42 degrees.