Let circle inscribe in square . Let be point lie on circle .

Prove that

Author: VanKhea, Cambodia

Filed under: Uncategorized ]]>

Let be incenter of an equilateral triangle . Let be any point and let be projection points from to the sides .

Prove that

Author: Van Khea, Cambodia

Filed under: Uncategorized ]]>

Let be circumcenter of an equilateral triangle and let be any point in the plan.

Prove that

Author: Van Khea, Cambodia

Filed under: Uncategorized ]]>

Given an equilateral triangle . Let is a line tangent to incircle . Let be projection points from to line .

Prove that

Author: Van Khea, Cambodia

Filed under: Uncategorized ]]>

Given an equilateral triangle . Let be any point lie on incircle.

Prove that

Author: Van Khea, Cambodia

Filed under: Uncategorized ]]>

is an equilateral triangle. lie on circumcircle and lie on incircle. are distances from and are distances from to .

Prove that

Author: Van Khea, Prey Veng, Cambodia

Filed under: Uncategorized ]]>

Let be any point inside of an equilateral triangle . Let be the projection from to . Let are the projections from to the line pass through .

Prove that

Author: Van Khea, Prey Veng, Cambodia

Filed under: Uncategorized ]]>

let be midpoints of . Let be any line and let be distances from to the line .

Prove that

Author: Van Khea, Prey Veng, Cambodia

Filed under: Uncategorized ]]>

.

Author: VanKhea

Generalization: RagvaloD

Filed under: Uncategorized ]]>

Let be collinears points on the sides .

Prove that if then

Author: Van Khea

Filed under: Uncategorized ]]>