### Video Transcript

Find the height of the circular segment π΄π·π΅ given π is a circle with a radius length of 18 centimeters, the line segment ππΆ is perpendicular to the line segment π΄π΅, and ππΆ is equal to 14 centimeters.

Well, the first thing weβre gonna do in this question is mark on the information weβve been given from the question onto our diagram. So, first of all, weβre told that π is a circle with a radius length of 18 centimeters. So therefore, we know that ππ΅ and ππ΄ are both going to be 18 centimeters because these are both the radius of our circle.

Then, weβre also told that the line segment ππΆ is perpendicular to the line segment π΄π΅. Weβve already been shown this in our diagram because we got this right angle here. And then, finally, weβre told that ππΆ is equal to 14 centimeters. Okay, great, so weβve now labeled every part of our diagram that we can. So, whatβs the next stage?

Well, what exactly are we looking to find out? Well, in this question, what weβre looking to find out is the height of the circular segment π΄π·π΅. Well, Iβve marked this on our diagram in orange. And this is the section from πΆ to π·. Well, we can see that ππ· is going to be the radius of our circle. So therefore, we can say that ππ· is equal to ππ΅, which is equal to ππ΄. And these are all equal to 18 centimeters. And thatβs because the radius of the circle is 18 centimeters.

So therefore, the section weβre looking for, which is πΆπ·, is gonna be equal to ππ· minus ππΆ. So therefore, we can say that πΆπ· is equal to 18 minus 14. So therefore, this is gonna be equal to four centimeters. So, we can say that the height of the circular segment π΄π·π΅ is four centimeters.