Can someone help me out with this?

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Can someone help me out with this? 2016-01-15 17:59:35 Post No. 33245

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Can someone help me out with this? 2016-01-15 17:59:35 Post No. 33245

[Report] Image search: [iqdb] [SauceNao] [Google]

Can't figure it out for some reason....

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>>33245

It isn't isoscles.

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>>33246

It is, sure of it. I think u need to take a point in the middle of AB and use that and probably also use Thales. I get somewhere but can finish it....

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>>33247

Can't*

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>>33246

Definitionaly, a triangle with two sides of identical length is isosceles.

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>>33245

Add the middle point M of the circle and segments MD and ME.

Now you see three isosceles triangles with bases opposites to M, namely

AMD with base angle say alpha

DME with base angle say delta

EMB with base angle say gamma

By adding the three angles at M we obtain

180° = (180° - 2alpha) + (180° - 2delta) + (180° - 2 gamma)

which implies alpha + delta + gamma = 180°

The triangle ABC is also isosceles which implies alpha + 2gamma = 180°, therefore delta = gamma.

Now look at D:

180° = alpha + delta + angle EDC which implies that the angle EDC is also gamma, just like the angle DCE = angle ACB.

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>>33267

*add also segment DE

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>>33267

what level of mathematics is this? Calculus 4?

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>>33281

You only need that the sum of the angles of a triangle is 180°, that the straight angle is 180°, and that an isosceles triangle has two equal sides and two equal angles, so basic geometry.

The problem can probably be solved differently.

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>>33281

are you kidding? this is highschool geometry

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>>33289

this guy has it

>>33267

this works, but you can make this even easier after step one by showing that segment ME is parallel to segment AC. This can be shown by using a couple of thales laws and that 180° makes a straight line. its pretty trivial at that point to show that ACB = CDE and therefore triangle DCE is isoscles

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>>33296

Aha that one is simpler yeah, so by just saying that the angles are the same you are also able to say that DCE is, just like ACB, isoscles right?

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>>33324

yeah, because isosceles can be defined by either two sides of the same length, or two base angles that are the same.

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>>33324

even moreso, through this method you are actually showing that angles ABC, ACB, CDE, ad ECD are all the same value. because of this they are similar triangles. this also proves that triangle DCE is isosceles.

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>>33332

amendment, triangles DCE and ABC are similar. sorry about that

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>>33335

Yea i figured :)

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