If the station goes on the circle, it will be the same distance from the supply hut as the others because all points on a circle are the same distance from the circle’s center.We know this triangle has a circumscribed circle because all triangles have one.The scientists should construct the circumscribed circle and put the new station anywhere on the circle.What should they do? Be sure these points come up in the discussion: Next, tell students that the scientists want to build another research station the same distance from the supply hut as the other stations. This point is equidistant from all the vertices of the triangle, because points on perpendicular bisectors of a segment are equidistant from the segment’s endpoints. The perpendicular bisectors will meet in one point.Central angles subtended by arcs of the same length are equal. The scientists should create the perpendicular bisectors of the sides of triangle \(RST\). Inscribed angles subtended by the same arc are equal.Be sure these points come up in the discussion: Parallel lines in shapes can form corresponding and. Angles can be calculated inside semicircles and circles. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the. What should they do? Challenge students to be precise in their use of language, and to explain why their ideas will work. Angles in a triangle add up to 180° and in quadrilaterals add up to 360°. Tell students that the points represent locations of 3 research stations in a desert, and that scientists want to build a supply hut that is the same distance from all 3 stations.
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