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Although words like "tangent" might sound complex at first, these concepts are actually quite simple when we can visualize how they work. Like many geometric concepts, tangent is something that can be easily illustrated and explained. What are congruent tangents and circumscribed polygons? Let's find out:

Let's start with congruent tangents. A tangent to a circle is simply a line that *touches* the edge of the circle without actually cutting through it. "Tangere" is the Latin verb for "touch," which helps us remember how this line works. The Latin word for "cut" is "secare," which is where we get the name "secant." Remember that if you see a line that "cuts through" a circle, you're looking at a secant line and *not* a tangent line.

But what happens when more than one line is tangent to a circle? Take a look:

If two lines emanate from the same exterior point (A) and are tangent to a circle, then we know that they are always congruent. Congruence is essentially just another word for equality. In this diagram, we can see that line AB is congruent to line AC.

Now let's add another concept into the mix: Circumscribed polygons. When we circumscribe something, we simply draw another shape around it. The Latin "circum" means "around," while "scribere" is the verb "to cut."

We can circumscribe polygons around a circle. Here's what that looks like:

When a polygon is circumscribed around a circle, we know that the vertices never lie *on* the circle itself. We also know that each side is tangent to the circle. Another interesting feature is that each side of the polygon touches the circle at its midpoint.

Common Core: High School - Geometry Flashcards

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