Geometric Mean

page revision: 0, last edited: 15 Sep 2008 09:04

Geometric Mean

page revision: 0, last edited: 15 Sep 2008 09:04

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187.Problem.…For consistency with Figure 190 and with the 2nd solution, the given segments should be

aandb(notaandc). Respectively, two lines below, there should beBC=b(notBC=c).ReplyOptionsThe ratio is equal to 3/4 (not 5/4, as incorrectly stated in the problem). This error is corrected though in problem 528, which is equivalent to problem 407.

.

ReplyOptionsthe square of a side of a triangle is equal to, greater than, or smaller than the sum of the squares of the other two sides, depending on whether the angle opposite to this side is right, acute, or obtuse.It looks like the square of the side should be smaller than the sum of the squares of the other two sides when the angle is acute, and greater when the angle is obtuse.

ReplyOptionsRight

ReplyOptionsI'm trying to solve problem 409. I've drawn a picture, and I have no idea how to proceed. Some guidance would be appreciated, or, barring that, a solution where I can follow it and understand it. I've managed to solve problems 404 and 402 prior to this, if that helps at all.

Problem 409 states: The diameter AB of a circle is extended past B, and at a point C on this extension CD perpendicular to AB is erected. If an arbitrary point M of this perpendicular is connected with A, and the other intersection point of AM with the circle is denoted A', then AM times AA' is a fixed quantity, i.e. it does not depend on the choice of M.

ReplyOptionsConnect A' with B.

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