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The Purification Crusade


I sadly never got the chance to solve these kind of things using English terminology, so please try to bear with my poor quality, sloppy, subpar explanation.

First you prove that ∠DBC = ∠EBA since AC crosses ED. Then you prove that △DBC and △EBA are similar as ∠DBC = ∠EBA, ∠CDB = ∠AEB and EB (1400ft.) is proportional to BD (700ft.). Finally, as △DBC and △EBA are similar, that means that DC is proportional to AE by the same ratio as EB is to BD. Which gives us:

x = DC(800) * (EB(1400) / BD(700)) = 1600



I can follow your process well enough, but I’m also needing the why and how connected; the rules which prove it.


@phoinexflame seems to have a good explanation.
Definitions quoted from quick googling.

What I learned as X angles.
“When two lines intersect, the opposite (X) angles are equal”

Similar shapes topic. “Having the same shape; having corresponding sides proportional and corresponding angles equal”.
Here you are trying to match equal angles as pairs.
∠DBC = ∠EBA : Explained by X angles
∠CDB = ∠AEB : Fact given in question
You could also say
∠BCD = ∠EAB : If you know 2 angles of a triangle you effectively know the third angle of a triangle. (All 3 angles of a triangle add to 180 degrees.)

Practically since the triangles are similar, one triangle is the same shape as the other by scaled to a different size. If something is scaled, everything is enlarged (or shrinked) to a fixed ratio.
Like how you can match angles as pairs, you can match corresponding sides of a shape.
AB & BC (BC unknown)
EB & BD (both known values)
x (AE) & DC (x unknown)

Then you just solve stuff using ratios.
(The scaling factor)
x / DC = EB / BD


You also should be careful not to get points deducted from not writing units :blush:.
So write the answer as x = 1600 ft.

If you google “similar shapes” you can probably find something.


You got bullied by your niece into doing her math homework? LUL. I’d call you a nerd, but clearly that’s not the case or you wouldn’t be asking for help. ROFL!


I recognize this question. It’s from an SAT practice test, if I recall correctly. Good luck to your niece on the test; I’m taking one this Saturday.


I feel safe now


Her fatal error, to be sure!

Thanks everyone! I will forward this to her. She is a quick learner, so I think she’ll be fine when she studies it for a bit.


Looks like a setup for a perfect Betrayal :persevere:.


I am late to the party, but I encourage you to directly mention me whenever you need smth like this to be solved. I’d be glad to help and it’s usually fun for me.

But only Maths, not Physics, please :wink:


I can (kinda) help with physics


Could be. But Maehvs are too busy betraying their babies to think of that.


I did honestly think about mentioning you, but I didn’t want to be presumptuous in your availability at the time. I will gladly do so in the future, given that the invitation has been issued!

Like I said previously, it pains me that solutions to math problems as simple as these have grown more elusive as I move farther away from my university days. I also realize that I could take steps to re-educate myself, but I am also very lazy…so…


Well, to advocate you, school level geometry isn’t simple. It requires memorization of lots of facts which an ordinary person would and should easily forget if not practiced regularly.

That said, I would suspect some kind of autism or another psychic anomaly from a person who remembers all school geometry without using it in daily life.


I can help with physics and math, but I’m bad at memorizing formulas


Anyone here tried Spellbreak?


I leave for a bit and this is what I COME BACK TOO?



I mean…
Who does that…
…the whole…expectations thing…:smirk:


Me. Its kinda fun if you are into the battle royale scene


It honestly depends from the BR if I enjoy it. I liked Realm Royale and Apex, while disliked Fortnite. First impressions from some gameplay i saw is very good


Vocal percussion on a whole nother level
Coming from my mind
Vocal percussion on a whole nother level
Coming from my mind