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Imagine a polygon (not necessarily convex) with 2015 sides. Suppose .pdf

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Imagine a polygon (not necessarily convex) with 2015 sides. Suppose there is a circle that has exactly one common point with each of its sides. None of the vertices of the polygon is a point of the circle. Prove that at least one of the sides is tangent to the circle. Solution Since sides of polygon tuches circle only once and vertices Do not tuches the circle. This implies that polygon is convex and circle is inside polygon (incircle ) .since by Def. Of tangent each side of polygon is tangent to the circle..

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Imagine a polygon (not necessarily convex) with 2015 sides. Suppose there is a circle that has exactly one common point with each of its sides. None of the vertices of the polygon is a point of the circle. Prove that at least one of the sides is tangent to the circle. Solution Since sides of polygon tuches circle only once and vertices Do not tuches the circle. This implies that polygon is convex and circle is inside polygon (incircle ) .since by Def. Of tangent each side of polygon is tangent to the circle.

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Imagine a polygon (not necessarily convex) with 2015 sides. Suppose .pdf

  • 1. Imagine a polygon (not necessarily convex) with 2015 sides. Suppose there is a circle that has exactly one common point with each of its sides. None of the vertices of the polygon is a point of the circle. Prove that at least one of the sides is tangent to the circle. Solution Since sides of polygon tuches circle only once and vertices Do not tuches the circle. This implies that polygon is convex and circle is inside polygon (incircle ) .since by Def. Of tangent each side of polygon is tangent to the circle.