MathDB

Let

ABC

be an equilateral triangle of side length

2

. Point

A'

is chosen on side

BC

such that the length of

A'B

k<1

. Likewise points

B'

and

C'

are chosen on sides

CA

and

AB

. with

CB'=AC'=k

. Line segments are drawn from points

A',B',C'

to their corresponding opposite vertices. The intersections of these line segments form a triangle, labeled

PQR

. Prove that

\Delta PQR

is an equilateral triangle with side length

{4(1-k) \over \sqrt{k^2-2k+4}}

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