Question Video: Finding the Height of a Circular Segment given Its Circle’s Radius Mathematics

Video Transcript

Find the height of the circular segment 𝐴𝐷𝐵 given 𝑀 is a circle with a radius length of 18 centimeters, the line segment 𝑀𝐶 is perpendicular to the line segment 𝐴𝐵, and 𝑀𝐶 is equal to 14 centimeters.

Well, the first thing we’re gonna do in this question is mark on the information we’ve been given from the question onto our diagram. So, first of all, we’re told that 𝑀 is a circle with a radius length of 18 centimeters. So therefore, we know that 𝑀𝐵 and 𝑀𝐴 are both going to be 18 centimeters because these are both the radius of our circle.

Then, we’re also told that the line segment 𝑀𝐶 is perpendicular to the line segment 𝐴𝐵. We’ve already been shown this in our diagram because we got this right angle here. And then, finally, we’re told that 𝑀𝐶 is equal to 14 centimeters. Okay, great, so we’ve now labeled every part of our diagram that we can. So, what’s the next stage?

Well, what exactly are we looking to find out? Well, in this question, what we’re looking to find out is the height of the circular segment 𝐴𝐷𝐵. Well, I’ve marked this on our diagram in orange. And this is the section from 𝐶 to 𝐷. Well, we can see that 𝑀𝐷 is going to be the radius of our circle. So therefore, we can say that 𝑀𝐷 is equal to 𝑀𝐵, which is equal to 𝑀𝐴. And these are all equal to 18 centimeters. And that’s because the radius of the circle is 18 centimeters.

So therefore, the section we’re looking for, which is 𝐶𝐷, is gonna be equal to 𝑀𝐷 minus 𝑀𝐶. So therefore, we can say that 𝐶𝐷 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 𝐴𝐷𝐵 is four centimeters.