CTK Insights

Existence of the Incenter: a Second Look

admin — Wed, 01 Feb 2012 17:59:11 +0000

The three angle bisectors of a triangle meet at incenter of the triangle. Reversing the problem we may ask a relevant question: Given three concurrent lines: α, β, and γ. Is there always a triangle with the three lines as the angle bisectors. If so, construct the triangle. Solution Given three concurrent lines: α, β, [...]

Existence of the Incenter: a Second Look is a post from: CTK Insights

Medians in a Triangle Meet at the Center: a Second Look

admin — Wed, 01 Feb 2012 17:39:58 +0000

The medians of a triangle meet at a point known at the center of the triangle. Reversing the problem we may ask a relevant question: Given three concurrent lines: α, β, and γ. Is there always a triangle with the three lines as the medians. If so, construct the triangle. Solution Given three concurrent lines: [...]

Medians in a Triangle Meet at the Center: a Second Look is a post from: CTK Insights

Altitudes Concur at a Point: a Second Look

admin — Mon, 30 Jan 2012 17:53:42 +0000

The altitudes of a triangle concur at a point - the orthocenter of the triangle. There are multitudes of proofs, each shedding light of a different hue on the existence of the orthocenter. Collecting these proofs was an enjoyable undertaking, and edifying, too. Not until a few days ago, when I came across another problem, [...]

Altitudes Concur at a Point: a Second Look is a post from: CTK Insights