### Video Transcript

Given that the measure of angle
π΅πΆπ΄ equals 61 degrees and the measure of angle π·π΄π΅ equals 98 degrees, can a
circle pass through the points π΄, π΅, πΆ, and π·?

Remember, if there are a pair of
congruent angles subtended by the same line segment and on the same side of it, then
their vertices and the segmentβs endpoints lie on a circle in which that segment is
a chord. Well, we have a line segment π΅π΄,
from which angle π΅πΆπ΄ and π΅π·π΄ are subtended. The angles lie on the same side of
that line segment. So if angle π΅πΆπ΄ is equal to
angle π΅π·π΄, then all four of our points must lie on the circumference of a
circle. Now, weβre given that the measure
of angle π΅πΆπ΄ is 61 degrees and the measure of angle π΅π΄π· is 98.

Since triangle π΅π·π΄ is isosceles,
we can calculate the measure of angle π΅π·π΄ by subtracting 98 from 180 and then
dividing by two. And that gives us that the measure
of angle π΅π·π΄ is 41 degrees. So we see that the measure of angle
π΅πΆπ΄ is not equal to the measure of angle π΅π·π΄. Since these angles are not equal,
we observe that a circle cannot pass through the points, and the answer is no.