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Intermediate

Big brother

Two squares and three line segments. What’s the angle α?

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Solution

The angle α is 45°.

Solution by Dmitriy Spiridonov.

Visual solution

Solution without words by David Andriana.

Poem

Big brother
An Orwell prophecy
Humans are malleable infinitely
Just stop the pain
Learning
Understanding by doing
And accepting
Human being are nothing
Every year fewer and fewer words
And meanings
Big brother is asking
And you are following
And you are lying
And you are dying

Bella

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2 replies on “Big brother”

ABCD is a square, clockwise with A at the left top. E is some point on BC. EFGC is another square, clockwise with E at left top. BG is joined. DE meets BG at H. CH is joined.

The triangles DCE and BCG are congruent. It gives angle EDC = angle GBC.

Thus quadrilateral BDCH is cyclic.
angle BDC + angle BHC = 180° = angle BHC + angle alpha.
angle BDC = angle alpha = 45°

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