DOIAbstract
We provide a simple visual proof of van Schooten’s theorem: given an equilateral triangle ABC with circumcircle, if point P is chosen on minor arc BC, then PA = PB + PC
We provide a simple visual proof of van Schooten’s theorem: given an equilateral triangle ABC with circumcircle, if point P is chosen on minor arc BC, then PA = PB + PC
noneThe top two sliders choose lengths of the legs of the right triangle. The third slider converts...
Knowledge about Plane GeometryLet P be a point outside a circle and PB and PD be two secants. Then P...
In Part I of this article we had narrated the history of this theorem and discussed a beautiful ‘pur...
Knowledge about plane geometry and trianglesLet ABC be an equilateral triangle and let P be a point ...
Knowledge about plane geometry and trianglesLet ABC be an equilateral triangle and let P be a point ...
Abstract. We give a proof of Floor van Lamoen’s theorem and its converse on the circumcenters of the...
Abstract. We give a proof of the famous Erdős-Mordell inequality using Ptolemy’s theorem. The follo...
Let ABC be a triangle and P be a point on the circumcircle of circumradius R. Let A' and B' be the p...
An elementary, yet evidently previously unnoticed, property of the equilateral triangle is presented...
In any triangle, the perpendicular side bisectors meet the corresponding internal angle bisectors on...
Floor van Lamoen has kindly pointed out that the necessity part of the main theorem of [1] does not ...
Carnot's theorem states that the signed sum of the perpendicular distances from the circumcenter of ...
Carnot's theorem states that the signed sum of the perpendicular distances from the circumcenter of ...
It is well known [2, p. 187] that two intersecting circles O(R) and O1(R1) are the circumcircle and ...
Morley's theorem asserts that the points of intersection of the adjacent angle trisectors of the ang...
noneThe top two sliders choose lengths of the legs of the right triangle. The third slider converts...
Knowledge about Plane GeometryLet P be a point outside a circle and PB and PD be two secants. Then P...
In Part I of this article we had narrated the history of this theorem and discussed a beautiful ‘pur...
Knowledge about plane geometry and trianglesLet ABC be an equilateral triangle and let P be a point ...
Knowledge about plane geometry and trianglesLet ABC be an equilateral triangle and let P be a point ...
Abstract. We give a proof of Floor van Lamoen’s theorem and its converse on the circumcenters of the...
Abstract. We give a proof of the famous Erdős-Mordell inequality using Ptolemy’s theorem. The follo...
Let ABC be a triangle and P be a point on the circumcircle of circumradius R. Let A' and B' be the p...
An elementary, yet evidently previously unnoticed, property of the equilateral triangle is presented...
In any triangle, the perpendicular side bisectors meet the corresponding internal angle bisectors on...
Floor van Lamoen has kindly pointed out that the necessity part of the main theorem of [1] does not ...
Carnot's theorem states that the signed sum of the perpendicular distances from the circumcenter of ...
Carnot's theorem states that the signed sum of the perpendicular distances from the circumcenter of ...
It is well known [2, p. 187] that two intersecting circles O(R) and O1(R1) are the circumcircle and ...
Morley's theorem asserts that the points of intersection of the adjacent angle trisectors of the ang...
noneThe top two sliders choose lengths of the legs of the right triangle. The third slider converts...
Knowledge about Plane GeometryLet P be a point outside a circle and PB and PD be two secants. Then P...
In Part I of this article we had narrated the history of this theorem and discussed a beautiful ‘pur...
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