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SAT Math Level 2 Subject Test Sample Question #26

asked 2010-10-20 05:18:26 -0500

ccanonc gravatar image

updated 2011-05-12 09:09:46 -0500

Kelvin Li gravatar image

A circle has a radius of 2. Two different tangent lines intersect the circle at points D and E. Those same tangent lines intersect each other outside the circle at point F, forming an acute angle of 50 degrees. If a chord is drawn between D and E, what is its length?

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answered 2010-10-20 09:40:22 -0500

Mike Hansen gravatar image

This isn't really a Sage question. The angle between the center of the circle C, point D (or E), and F is a right angle. Thus, the angle DCE is 180 - 50 = 130 degrees. Half of the chord DE is a side of a right triangle opposite an angle of 130 / 2 = 65 degrees. Using the formula for sin and doubling we get the chord length to be

sage: 2*(2*sin(65/360*2*pi))
sage: _.n()
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Nope, it's an SAT question. And the questions were slowing down, so it bumped the traffic up a bit...and the exercise sometimes brings up other issues. Are you saying sage shouldn't be used for teaching, or problems you don't like shouldn't be asked?

ccanonc gravatar imageccanonc ( 2010-10-20 10:08:43 -0500 )edit

Sage should be used for teaching, and this website should be used for teaching about Sage. But, I don't think this website should really be used for teaching math or solving homework problems. While it may have bumped the traffic up, the question and answer probably weren't useful to anyone.

Mike Hansen gravatar imageMike Hansen ( 2010-10-20 11:27:25 -0500 )edit

It does teach about sage, but you're the admin, so if you want to pull rank, just delete my post. Vive le Censorship.

ccanonc gravatar imageccanonc ( 2010-10-20 12:09:26 -0500 )edit

I think that Mike's point is just that can't be all things to all people. Until it gets a little more off the ground, it's wise to make it focused; otherwise it's confusing as to what it is. That said, if Sage really brings insight to an SAT or GRE problem, bring it on!

kcrisman gravatar imagekcrisman ( 2010-10-20 15:54:57 -0500 )edit

For instance, on a Geogebra site, this question would be great, because you can construct the items in question. The only part Sage can do here is approximate. Some GRE question asking people to demonstrate the Cayley tables of two non-isomorphic groups of order four would be perfect, though!

kcrisman gravatar imagekcrisman ( 2010-10-20 15:58:03 -0500 )edit

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Asked: 2010-10-20 05:18:26 -0500

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Last updated: Oct 20 '10