### Video Transcript

Given that the points π΄, π΅, πΆ,
and π· lie on a circle, find the length of segment π΅π΄.

So weβd like to find this length of
the segment. And we are also told that π΄, π΅,
πΆ, and π· lie on a circle, so maybe something like this. Since we have two lines containing
the two segments π΅π΄ and πΆπ· intersecting at point πΈ, we can use this to solve
for the length of πΈπ΄. And solving for the length of πΈπ΄
will help us find the length of π΅π΄.

To do so, we can use the fact that
πΈπ΄ times πΈπ΅ will be equal to πΈπΆ times πΈπ·. And again, finding this length πΈπ΄
is whatβs going to help us find the length of π΅π΄. So we can go ahead and write πΈπ΄
because we donβt know what it is. And the length of πΈπ΅ is 36. The length πΈπΆ we can actually
find, because all we need to do is take 39 centimetres plus 33 centimetres to give
us 72 centimetres. Thatβs the length of πΈπΆ. And then, lastly, we need to
multiply by πΈπ·, which is 33 centimetres.

So we can begin solving for πΈπ΄ by
multiplying 72 and 33 on the right-hand side of the equation. 72 times 33 is 2367. So now to solve for πΈπ΄, we divide
both sides of the equation by 36. And we find that the length of
segment πΈπ΄ is 66 centimetres.

And now we can use this to find the
length of π΅π΄. And this is because the length of
π΅π΄ will be equal to πΈπ΄ minus πΈπ΅. πΈπ΄ we found to be 66
centimetres. πΈπ΅ is 36 centimetres. So subtracting those, we find that
the length of segment π΅π΄ would be 30 centimetres.