Find the radius of the circle. CAN'T COPY THE GRAPH |...

Name: Problem 15, Chapter 11: Discovering Geometry an Investigative Approach
Uploaded: 2022-02-01T16:55:34-08:00
Duration: 5 min 24 s
Channel: Avi Zellman
Description: Find the radius of the circle. CAN'T COPY THE GRAPH

Key Concepts

Graphical Interpretation

Graphical interpretation in geometry involves analyzing visual representations, such as drawings or graphs, to extract relevant information. Recognizing the center, points on the circle, and corresponding distances allows for the determination of the circle's radius even when numerical coordinates or labels are provided graphically.

Circle

A circle is a set of points in a plane that are all at a constant distance from a fixed center point. Understanding the geometric properties of circles is essential for computing measurements such as areas or circumferences, and for solving problems involving circular shapes.

Radius

The radius of a circle is the distance from its center to any point on its circumference. It is a crucial measurement that is used in various formulas related to circles, such as those computing the area and circumference.

Transcript

00:01 All right, let's take a look at a question where we're being asked to find the radius of a circle.

00:06 I'm trying to find r.

00:09 What does r equal? we're given some information.

00:13 The first thing that we're given is a relationship.

00:16 So the circle, let's draw in our radius.

00:24 The circle has this radius drawn in, but with an unknown amount, but it's split.

00:31 It's split at a right angle.

00:37 And we're given that the distance from where those lines intersect is three to the edge, and that perpendicular, that line is five.

00:54 So with just those two pieces of information, we can actually solve what the radius is equal to.

01:04 And the way that we're going to do that is by adding in another line here, to find a triangle, a right triangle.

01:14 So i'm going to put in this dashed radius.

01:21 And now let's put in some variables, things that we don't know.

01:25 So we know the red radius that was drawn in had some portion of it that was three, but this other missing portion we're not sure of.

01:35 So let's call that x because it's unknown.

01:40 And calling that distance x means that we do know what the length of a radius is because it's just the combination of those two values, three and x.

01:51 So over here on our dash line, we can now label this as three plus x.

01:59 And that's our hypotenuse, if you will, of that little triangle.

02:04 So if you pull this triangle out, i'll redraw it over here.

02:09 We can use the pythagorean theorem to help us solve for the missing value.

02:16 So our long side is five.

02:20 The short side, again, is that x, and then the hypotenuse was 3 plus x.

02:26 So let's use the pythagorean theorem.

02:29 Just a reminder, it's the two legs, five and x, each squared and then added together to equal the square of the hypotenuse.

02:37 So 5 squared plus x squared equals 3 plus x squared.

02:48 So nothing really to do on the left hand side.

02:51 You can simplify the 5 squared into 25, 25 plus x squared.

02:56 3 plus x squared.