Plane and solid geometry . ion XII. Theorem 320. If two tangents are drawn -11^07)% any given -pointto a circle, these tangents are equal. Given FT and PS^ two tangents from point P to circle 0. To prove FT=PS. The proof is left as an exercise for the student. Ex. 446. The sum of two opposite sides of a circumscribed quadrilat-eral is equal to the sum of the other two sides. Ex. 447. The median of a circumscribed trapezoid is one fourth theperimeter of the trapezoid. Ex. 448. A parallelogram circumscribed about a circle is either arhombus or a square. Ex. 449. The hypotenuse of a right triangl
Plane and solid geometry . ion XII. Theorem 320. If two tangents are drawn -11^07)% any given -pointto a circle, these tangents are equal. Given FT and PS^ two tangents from point P to circle 0. To prove FT=PS. The proof is left as an exercise for the student. Ex. 446. The sum of two opposite sides of a circumscribed quadrilat-eral is equal to the sum of the other two sides. Ex. 447. The median of a circumscribed trapezoid is one fourth theperimeter of the trapezoid. Ex. 448. A parallelogram circumscribed about a circle is either arhombus or a square. Ex. 449. The hypotenuse of a right triangle circumscribed about acircle is equal to the sum of the other two sides minus a diameter of thecircle. Ex. 450. If a circle is inscribed in any triangle, and if three trianglesare cut from the given triangle by drawing tangents to the circle, thenthe sum of the perimeters of the three triangles will equal the perimeterof the given triangle. BOOK II 129 Proposition XIIL Problem321. To inscribe a circle in a given Given A ABC. To inscribe a circle in A AB C, I. Construction 1. Construct AE and CD, bisecting A CAB and BCA, respec^tively. § 127. 2. AE and CD will intersect at some point as 0. § 194 3. From 0 draw OF l^AC. § U9. 4. With 0 as center and OF as radius construct circle FGH. 5. Circle FGH is inscribed in A ABC. II. The proof and discussion are left for the student. 322. Def. A circle which is tangent toone side of a triangle and to the other twosides prolonged is said to be escribed to thetriangle. Ex. 451. Problem. To escribe a circle to agiven triangle. Ex. 452. (a) Prove that if the lines that bi-sect three angles of a quadrilateral meet at a com-mon point P, then the line that bisects the remaining angle of the quadri-lateral passes through P. (6) Tell why a circle can be inscribed in thisparticular quadrilateral. Ex. 453. In triangle ABC, draw XY parallel to PC so that XY-\-BG=BX^ CY. Ex. 454. Inscribe a circle in a given rhombus.
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
