# This is probably really simple but they didn't word it right :(

• Sep 16th 2007, 03:48 PM
peachgal
This is probably really simple but they didn't word it right :(
Okay I don't get this:

http://i4.photobucket.com/albums/y10...ous/circle.jpg

The diagram above shows a flat surface containing a line and a circle with no points in common. Can you visualize moving the line and/ or circle so that they intersect at exactly one point? Two points? Three points? Explain each answer and illustrate each with an example when possible.

And...

$\displaystyle 3x/4=6/7$

And...

http://i4.photobucket.com/albums/y10...s/triangle.jpg

The perimeter (the sum of the side lengths) of the triangle above is 52 units. Write and solve an equation based on the information in the diagram. Use your solution for x to find the measures of each side of the triangle. Be sure to confirm that your answer is correct.

• Sep 16th 2007, 06:33 PM
DivideBy0
I don't believe a line can intersect a circle at three points, but they sure can at two. When a line touches a circle at one point it is called a tangent. When a line touches at two points it is called a secant. See the attached diagram (thanks wikipedia). Don't confuse secant with chord. A chord is a line segment, while a secant is a line. So the secant keeps on going while a chord stops at the circumference.

To solve for x in:

$\displaystyle \frac{3x}{4}=\frac{6}{7}$

Multiply both sides by 4,

$\displaystyle 3x=\frac{24}{7}$

Then divide both sides by 3,

$\displaystyle x=\frac{8}{7}$

For the triangle, we know the perimeter is 52, so
$\displaystyle (7x-4)+(10x+3)+19=52$
$\displaystyle 17x+18=52$
$\displaystyle 17x=34$
$\displaystyle x=2$
• Sep 16th 2007, 07:53 PM
peachgal
Quote:

Originally Posted by DivideBy0
I don't believe a line can intersect a circle at three points, but they sure can at two. When a line touches a circle at one point it is called a tangent. When a line touches at two points it is called a secant. See the attached diagram (thanks wikipedia). Don't confuse secant with chord. A chord is a line segment, while a secant is a line. So the secant keeps on going while a chord stops at the circumference.

To solve for x in:

$\displaystyle \frac{3x}{4}=\frac{6}{7}$

Multiply both sides by 4,

$\displaystyle 3x=\frac{24}{7}$

Then divide both sides by 3,

$\displaystyle x=\frac{8}{7}$

For the triangle, we know the perimeter is 52, so
$\displaystyle (7x-4)+(10x+3)+19=52$
$\displaystyle 17x+18=52$
$\displaystyle 17x=34$
$\displaystyle x=2$

Thanks for the thorough answers genius! Love ya!