# Video: Finding the Height of a Circular Segment given Its Circleβs Radius

Find the height of the circular segment π΄π·π΅ given π is a circle with a radius length of 18 cm, the line segment ππΆ β₯ the line segment π΄π΅ and ππΆ = 14 cm.

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### 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 ππΆ is perpendicular to the line segment π΄π΅, and ππΆ is equal to 14 centimeters.

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

Then, weβre also told that the line segment ππΆ is perpendicular to the line segment π΄π΅. Weβve already been shown this in our diagram because we got this right angle here. And then, finally, weβre told that ππΆ is equal to 14 centimeters. Okay, great, so weβve now labeled every part of our diagram that we can. So, whatβs the next stage?

Well, what exactly are we looking to find out? Well, in this question, what weβre looking to find out is the height of the circular segment π΄π·π΅. Well, Iβve marked this on our diagram in orange. And this is the section from πΆ to π·. Well, we can see that ππ· is going to be the radius of our circle. So therefore, we can say that ππ· is equal to ππ΅, which is equal to ππ΄. And these are all equal to 18 centimeters. And thatβs because the radius of the circle is 18 centimeters.

So therefore, the section weβre looking for, which is πΆπ·, is gonna be equal to ππ· minus ππΆ. So therefore, we can say that πΆπ· 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.