A complete and practical solution book for the common school teacher . FIG. 61. )/2V 3 = 130 PROBLEM a point without a circle two tangents are drawn, formingwith each other an angle of 60°, and the length of each tangent is 20in.: what is the diameter? Solution. (1) Let DB and AB, the tan- gents = 20 ft., and the an-gle ABD=60°. (2) The angle A is a right triangle because it isformed by a tangent andradius. (3) OB bisects the angle DBA; hence, angle ABO=30°, K1( 62 and angle BOA=60°. (4) .*. The triangle BAO = half of an equilateral triangle whose sides are equal to OB. (5) OA=^OB. AB
A complete and practical solution book for the common school teacher . FIG. 61. )/2V 3 = 130 PROBLEM a point without a circle two tangents are drawn, formingwith each other an angle of 60°, and the length of each tangent is 20in.: what is the diameter? Solution. (1) Let DB and AB, the tan- gents = 20 ft., and the an-gle ABD=60°. (2) The angle A is a right triangle because it isformed by a tangent andradius. (3) OB bisects the angle DBA; hence, angle ABO=30°, K1( 62 and angle BOA=60°. (4) .*. The triangle BAO = half of an equilateral triangle whose sides are equal to OB. (5) OA=^OB. ABz=OAV3. 20 (6) .. AOV3 = 20, or OA=—==+ in. (7) in., the PROBLEM horse is tethered from one corner of a square 20-acre field: howlong must the rope be so that it can graze over 20 acres outside the field? 182 FAIRCHILDS SOLUTION BOOK. (1) (2) Solution. Let AOCB be the field, and Othe point at which horse theis tied. Let R = OH, the radius or thelength of the rope by whichthe horse is tied.
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Keywords: ., bookcentury1800, bookdecade1890, booksubject, booksubjectgeometry
