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Course: Math for fun and glory>Unit 3

Lesson 1: 2013 AMC 10 A

2013 AMC 10 A #22 / AMC 12 A #18

Video by Art of Problem Solving.  Problem from the MAA American Mathematics Competitions. Created by Art of Problem Solving.

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• What is tangency?
• The angle between two curves at a point where they intersect is defined as the angle between their tangent lines at that point.
• I'm a 6th grader trying to learn ahead of my grade any help on how to understand this plz?
• how much did the eight sphere measure or what ever?
• what is he using to draw on
it is really cool
• its a smart board and he's using a software called "Geo-Gebra"
(1 vote)
• I still do not get the concept of tangency?
Can anyone explain this to me?
I can't get any of the previous explanations..
• A tangent is an object, like a line, which touches a curve. The tangent only touches the curve at one point. That point is called the point of tangency
• Can anybody tell me whats a radll??
• Radii is plural for radius. (Therefore, you do not say "a radii.") The radius is basically half the diameter of a circle (the longest straight line that can fit in a circle).
• What grade and age is this for?
(1 vote)
• It's a high school math competition, although that doesn't mean middle schoolers can't participate. The AMC 10 is for 10th graders and below, AMC 12 is for 12th graders and below. However, this particular problem is on both the AMC 10 and 12 (there's usually some overlap), but yeah it's mainly for high schoolers.
(1 vote)
• Can someone just explain to me what happened? What's externally tangent? Also, I didn't even get the question. At first, I didn't even know there was an 8th sphere until he told us. I mean, I'm a 5th grader, and I'm still taking AMC 8, so I shouldn't feel bad..... right?
(1 vote)
• How can you answer this question if it is too hard?
(1 vote)
• True or keep on trying and don't give up. Just think of giving up as throwing your life away
(1 vote)
• When we originally drew the first cross section, how did we know that the 8th sphere did not pass through it?
(1 vote)