Inscribed angle "V" and whose sides pass through points "A" and "B". Draw line "OA". Angle "BOA" is a central angle; call it "θ". Lines "OV" and "OA" are both radii of the circle, so they have equal lengths. Therefore, triangle "VOA" is isosceles, so angle "BVA" (the inscribed angle) and angle "VAO" are equal; let each of them be denoted as "ψ". Angles "BOA" and "AOV" are supplementary. They add up to 180°, since line "VB" passing through "O" is a straight line. Therefore, angle "AOV" measures 180° − "θ". It is known that the three angles of a triangle add
How Are Things in Glocca Morra? made up by composer Lane, who had devised a dummy lyric beginning with the line, "There's a glen in Glocca Morra". Harburg liked the name but insisted on changing the line to "How are things in Glocca Morra?" because this is personal and immediately evocative of nostalgia and homesickness. James Stephens' work "The Crock of Gold" (first published in 1912) refers to "the leprechauns of Gort na Gloca Mora" ("the field of the big rock" in Gaelic). It is unknown whether Lane or Harburg were aware of the novel or if this is a coincidence. Many versions of this song