Find the area of the circle shown. CAN'T COPY THE FIGURE |...

Name: Problem 17, Chapter 13: Geometry for Enjoyment and Challenge
Uploaded: 2021-08-17T19:14:24-08:00
Duration: 5 min 33 s
Channel: Debasish Das
Description: Find the area of the circle shown. CAN'T COPY THE FIGURE

Key Concepts

Area Formula for a Circle

The area of a circle is calculated using the formula A = ?r², where r represents the radius and ? is a constant approximately equal to 3.14159. This concept is crucial in geometry when determining the space enclosed by a circular boundary.

Circle Geometry

A circle is a set of points in a plane that are all equidistant from a fixed point called the center. This basic understanding of circle geometry sets the stage for further calculations, such as computing its area or circumference.

Radius and Diameter

The radius of a circle is the distance from the center to any point on the circle, and the diameter is twice that length. These measurements are fundamental since many formulas, including the area formula, rely on the radius.

Transcript

00:01 Question number 17 here we are given a diagram yes let us draw the diagram first that is a circle so this given that this is the x -axis this is the sorry this is the y this is y this is y so this is y so that is so that is a point this is zero zero this is eight zero and that is a point it's five three okay so now you have to find the equation to circle so let us say assume that this is the enter c this is the line a b and is the point d so now you can see that so this is the center this is the ab is the core now suppose i draw a perpendicular here so this point is e so what will happen so this and this will be same right right so you can see this is so you can see this then what is the coordinate of e a you will be 4 .0 then what will happen this on this line a central line so center c can be that x coordinate will mean same only y can only y can only let us say 4 y so what will happen uh it will assume center is equal to c okay e c is perpendicular to a, b, right? then you can see a is, you can clearly say that a .e is equal to b, you know, center lies on ec line, right? hence, x coordinate of c will be 4.

02:41 Now that, let's assume c is equal to 4.

02:50 Y c is equal to 4 y so now what will do we'll try to see that if c is equal to 4 y the distance of c from so any point within the circle will be same so this line ac will be equal to cd so ac will be equal to cd so what is ac is is equal to s is equal to four square plus y square cd is equal to four minus five square square plus y minus three square right now let us solve this further so what will get we'll get you'll get 16 plus y square is equal to one plus y square minus 6y plus 9 so now you can write uh vice versa again since so minus 6y plus 10 is equal to 16 now you can write 6y is equal to minus 6 and plus y is equal to minus 1 now from that you just scored that center c is equal to 4 minus 1 right now you got the center so now the radius then we'll find can find the area okay so radius equal to you can see radius equal to your you go see this line it will be ac right ac so is equal to four square so it will be about 17 so area is equal to five 5 into root 70...

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