I need help with this Geometry problem.

[sick trail]

i used yandex to translate so it might be wrong at some words. If u have trouble understand them ill send u the original language.
Here’s the question:

Let ABC be the pointed triangle with the center of the outer line O. Call A ' the heart of the road
through C and exposure AB at A, call B ' is the center of the path that passes through A and contact BC at B, call
C ' is the center of the road that passes through B and exposes CA at C.
a) prove that the A'b'c'Triangle area is greater than or equal to the ABC Triangle area.
B) Call X, Y, Z respectively the perpendicular projection of O onto the lines a'b', B'c', C'a'.
Know that the XYZ triangle adjoins the straight lines in turn
A 'B', B'C', C' A'at points X', Y', Z' (X' X,Y 'Y,Z' Z). Prove that the
straight line ax', by', CZ' congruent.

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[lavish topaz]

Yes; send the original language, please.

[sick trail]

here

the original language is Vietnamese

[lavish topaz]

Oh, Vietnamese? Okay. Vậy thì đợi một xíu để mình dich ra hen. Nếu là sai nói vậy nha.

There is a lot of strange language in the translated text, and I am certain that it is not correct.

[sick trail]

well alright

[lavish topaz]

Let ABC be an acute triangle with the center of the circumscribed circle O. Let A' be the center of the circle passing through C and touching AB at A, let B' be the center of the circle passing through A and touching BC at B, call
C' is the center of the circle passing through B and touching CA at C.

Yes?

If that's the case, I don't understand. I assume that the prime symbol in this case represents a transformation of the original triangle ABC, but how can A'B'C' all be the center of the circle? They are all points, correct?

[sick trail]

well yep

[lavish topaz]

Hm, okay. The two ideas I have are the usages of Excircles and Perpendicular Projections, but I cannot understand the problem well enough to interpret it correctly. Let me think about it for a while.

In the mean time, please take those two topics (Đường tròn bàng tiếp trong tam giác và hình chiếu) into consideration, as I think you will need them.

[sick trail]

did u draw them?

to solve this u need to draw them

lemme show u

one sec

[sick trail]

here

@lavish topaz heres the picture

5 circles is wild

[urban lantern]

@sick trail 🖐️

[sick trail]

hii

could u help me with this

[urban lantern]

Yes, kindly add me

[sick trail]

added

[sick trail]

+close

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