Online Course Discussion Forum

MCIII Geo help

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MCIII Geo help
by Kevin Song - Wednesday, October 19, 2022, 8:28 PM

I don't know how to do 3.12, 3.13, 3.14, and 3.15 (2.)

For 3.12 I tried to split the trapezoid up but that didn't really help.

For the rest I have no clue

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Re: MCIII Geo help
by Dr. Kevin Wang - Thursday, October 20, 2022, 10:56 AM

3.12 is one of the harder questions with area transformation.  To start, let $Q$ be the midpoint of $CD$ and try to connect some midpoints to form parallel lines, then transfer the areas around. 

3.13 Use homothety: verify that triangles $ABC$ and $O_1O_2O_3$ are homothetic with center $P$.

3.14 Use translation to move the lines so that all the lines pass through the same point.

3.15 (2) You need to solve (1) first by translating the segments together; this process actually give you some ideas on how to cut up the new triangle and calculate the areas. In fact, the question only provides that the triangle $ABC$ has area 10, so that is the only information you need for the new triangle's area.

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Re: MCIII Geo help
by Kevin Song - Friday, October 21, 2022, 6:05 PM

Can I have hints on 3.20,3.22,3.23,3.25,3.26,3.27, as well as the solution for 3.12?