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

$\displaystyle (7x-4)+(10x+3)+19=52$

$\displaystyle 17x+18=52$

$\displaystyle 17x=34$

$\displaystyle x=2$