Let be points lies on .

Let such that and Let such that .

The same ways we get and .

Prove that

Author: Van Khea, Cambodia

]]>Let be circumcenter of an equilateral triangle and let be circumcenter of . Let tangent to at . are projection points from to . are projection points from to .

Prove that

Author: Van Khea, Cambodia

]]>Let be point lie on arc of an equilateral triangle such that . Let and be points such and .

Prove that

Author: Van Khea, Cambodia

]]>be midpoints of an equilateral triangle . be point lie on incircle of .

Prove that

Author: Van Khea, Cambodia

]]>Line tangent to incircle of an equilateral triangle at .

Prove that

Author: Van Khea, Cambodia

]]>is an equilateral triangle. Prove that:

Author: Van Khea, Cambodia

]]>Let .

Prove that

Author: Van Khea, Cambodia

]]>Let be circumcenter of triangle .

Prove that:

Author: Van Khea, Cambodia

]]>

Let be midpoints of an equilateral triangle . Let be midpoint of . Prove that:

Author: Van Khea, Cambodia

]]>is an equilateral triangle.

is midpoints of and

Prove that

Proposed by Van Khea, Cambodia

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