Incircle and excircles of a triangle polygon with any number of sides that has an inscribed circle—one that is tangent to each side—is called a tangential polygon. Incircle and excircles of a triangle In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three
All that is gold does not glitter and danger. Line seven refers to the sword Narsil. Line eight foreshadows the crownless Aragorn's accession to the throne of both the kingless Gondor and the vanished Arnor. Older editions of "The Lord of the Rings" indexed the poem as "The Riddle of Strider". From the 50th anniversary edition of 2005 on, the new, enlarged index by Wayne G. Hammond and Christina Scull list it as "All that is gold does not glitter". Early versions of the poem are recorded in "The Treason of Isengard", part of "The History of Middle-earth" book series by Christopher Tolkien. The first draft of