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Geometry Difficulty 3.5 AMC 10/12 Find the answer Canada

In $\triangle ABC$ , points
$D$ and $E$ lie on $AB$ , as shown.

If $AD=DE=EB=CD=CE$ , the measure
of $\angle ABC$ is

Pick one

Solution

A circle with radius $2$ has
area $\pi\times2^2=4\pi$ .

If the radius is tripled, then the new radius is $3\times2=6$ .

A circle with radius $6$ has area
$\pi\times6^2=36\pi$ .

The area of the original circle divided by the area of the new circle is
$\frac{4\pi}{36\pi}=\frac{4}{36}=\frac19$ .

Want a route through all this instead of an archive? The track puts 2,444 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.