What I need help with is figuring out what formula/function I need to put in the

Question

What I need help with is figuring out what formula/function I need to put in the Answer box so that it will give an answer of "inside", "outside", or "On the Circle". I was given the following information:

You are going to prepare a solution to answer the following problem using Microsoft Excel:

-- A circle is centered at point A (XA, YA) {you don't know in advance where this is}

-- It has a radius of r {you don't know in advance what the value is}

-- A second point is located at B (XB, YB){you don't know in advance where this is}

-- Is Point B inside, outside, or on the circle?

Stop here for a moment and re-read this and consider a simple example (sketching this out might help). If Point A is at the origin (0,0) and the radius r=3, then clearly if point B is (1,1) it is inside the circle; if point B is (5,5) it is outside the circle; and if point B is (0,3) or (3,0) it would be on the circle.

You may also need some additional guidance on how to approach this problem. Some helpful hints:

-- How do you measure distance between points A and B? Consider using the distance formula. Consider this function: =SQRT

-- How do you know if this distance is shorter, longer, or the same? Consider this function: =IF

-- Test your solution as you work through this with cases you know the answer to. For example, pick two points that you know (or can calculate) the distance between Point A and Point B.

A few ground rules so you do not need to test for certain errors:

-- I will type numbers for Point A, radius r, and Point B in the locations shown provided in the template

-- You may use any other space on the spreadsheet to perform calculations

-- You will tell me if the answer is Inside, Outside, or On the circle in the location provided in the template

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Explanation / Answer

I hope you're familiar with the equation of a cirlce with its center at (0,0) origin in general, which is:

f(x,y) = x2 + y2 - R2 , where R is the Radius.

Using co ordinate geometry, we can find that if a point P(x1,y1) satiesfiies the equation f(x,y) or f(x1,y1) = 0

or, x12 + y12 - R2 = 0 , it is on the circle

if, x12 + y12 - R2 < 0 , it is inside the circle boundary

if, x12 + y12 - R2 > 0 , it is outside the circle boundary

NOW, IF THE CENTER IS NOT IN ORIGIN.

we change the value of x in f(x,y) with x + xc , where xc is the x cordinate of the center of the circle

and we change the value of y in f(x,y) with y + yc , where yc is the y cordinate of the center of the circle.

So, now the equation becomes,

(x + xc)2 + (y + yc)2 - R2 , where (xc ,yc) is the center of circle and R is the radius

For a point P(x1,y1):

if, (x1 + xc)2 + (y1 + yc)2 - R2 = 0 , it is on the circle

if, (x1 + xc)2 + (y1 + yc)2 - R2 < 0 , it is inside the circle boundary

if, (x1 + xc)2 + (y1 + yc)2 - R2 > 0 , it is outside the circle boundary

you need to put the above formula to determine the point's location.

FEEL FREE TO COMMENT AND ASK QUERIES. HOPE THIS HELPS

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