Explaining the Yes/No Response in Two Points on a Circle

In summary, the conversation is discussing the placement of point C on a circle based on the positions of points A and B. It is explained that if the sum of the x components of OA and OB (vectors from point O to A and B) is equal to the radius, then point C will lie on the circle. If the sum is less than the radius, point C will be inside the circle.
  • #1
blimkie
111
0
http://putfile.com/pic.php?pic=10/30314175469.jpg&s=x11

if anyone would like to explain this to me that would be excelent and most appreciated

i know that a and b are both "yes" but i i don't know why or how to explain it

thanks
kyle
 
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  • #2
How, exactly, do you know both a and b are "yes?"
 
  • #3
wouldnt point c be on the circle if points a and b were separated a certain distance
 
  • #4
Lets call OC the x-axis and the y-axis is perpendicular to it. since the y components will always cancel out, the length of OC will be the sum of the X components of each vector (OA,OB). For OC to be on the circle its length has to be equal to the radius, so OC will be on the circle if the sum of OA's and OB's x components equal r (radius), for example if they each make a 60 deg. angle with the x-axis (.5r + .5r = r). For OC to lie inside the circle its length has to be less than r, this can happen if the sum of the x components is less than r, for example, OA and OB each make a more than 60 deg. angle with the x axis.
 
  • #5
thanks a lot daniel_i_l that explains it better than i could
 

1. What is a circle?

A circle is a shape that is defined by a set of points that are all equidistant from a single central point. It can also be described as the locus of all points that are a fixed distance away from a central point.

2. What are two points on a circle?

Two points on a circle are any two distinct points that lie on the circumference of the circle. They are equidistant from the center of the circle and are connected by a straight line segment called a chord.

3. How do you find the distance between two points on a circle?

The distance between two points on a circle can be found using the formula: d = 2r sin(a/2), where d is the distance, r is the radius of the circle, and a is the angle between the two points measured in radians.

4. Can two points on a circle be on opposite sides of the circle?

Yes, two points on a circle can be on opposite sides of the circle. This means that the distance between the two points is equal to the diameter of the circle.

5. How many possible pairs of points can be chosen from a circle?

There are an infinite number of possible pairs of points that can be chosen from a circle. This is because any two distinct points on the circumference of the circle can be chosen as long as they are not the same point or directly opposite each other.

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