Question Video: Finding the Length of a Chord Using the Chords Theorem Mathematics • 11th Grade

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

01:59

Video Transcript

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

So weβd like to find this length of the segment. And we are also told that π΄, π΅, πΆ, and π· lie on a circle, so maybe something like this. Since we have two lines containing the two segments π΅π΄ and πΆπ· intersecting at point πΈ, we can use this to solve for the length of πΈπ΄. And solving for the length of πΈπ΄ will help us find the length of π΅π΄.

To do so, we can use the fact that πΈπ΄ times πΈπ΅ will be equal to πΈπΆ times πΈπ·. And again, finding this length πΈπ΄ is whatβs going to help us find the length of π΅π΄. So we can go ahead and write πΈπ΄ because we donβt know what it is. And the length of πΈπ΅ is 36. The length πΈπΆ we can actually find, because all we need to do is take 39 centimetres plus 33 centimetres to give us 72 centimetres. Thatβs the length of πΈπΆ. And then, lastly, we need to multiply by πΈπ·, which is 33 centimetres.

So we can begin solving for πΈπ΄ by multiplying 72 and 33 on the right-hand side of the equation. 72 times 33 is 2367. So now to solve for πΈπ΄, we divide both sides of the equation by 36. And we find that the length of segment πΈπ΄ 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 πΈπ΄ minus πΈπ΅. πΈπ΄ we found to be 66 centimetres. πΈπ΅ is 36 centimetres. So subtracting those, we find that the length of segment π΅π΄ would be 30 centimetres.