A complete and practical solution book for the common school teacher . n.; through a point 10 in. from the cen-ter, tangents are drawn: find the lengths of these tangents, and alsothe chord joining the points of contact. Solution. (1) Let O be the center of the given circle, and P thegiven point. (2) On OP as a diameter describe a circumference at B and C. (3) Draw BO and CO. (4) Angles OBP and OCP are right angles, being inscribedin a semicircle. (5) OP is 10 in,; OB, 6 in. (6) BP or CP, V(102— 62)=8 in. (7) Area of OBP is(8x6)-^2 = 24 sq. in., and its altitude BD = (24x2)-=-10=48in. (8) Henc
A complete and practical solution book for the common school teacher . n.; through a point 10 in. from the cen-ter, tangents are drawn: find the lengths of these tangents, and alsothe chord joining the points of contact. Solution. (1) Let O be the center of the given circle, and P thegiven point. (2) On OP as a diameter describe a circumference at B and C. (3) Draw BO and CO. (4) Angles OBP and OCP are right angles, being inscribedin a semicircle. (5) OP is 10 in,; OB, 6 in. (6) BP or CP, V(102— 62)=8 in. (7) Area of OBP is(8x6)-^2 = 24 sq. in., and its altitude BD = (24x2)-=-10=48in. (8) Hence, the chord is 96 in., and one of the tangents 8 in. PROBLEM horse is tethered to one corner of a barn 40 ft. square, by a rope100 ft. long: over how much ground can he graze? Solution. (1) Let ADCO be the barn, and OF the rope 100 ft. long. (2) The area of E?;F=f of 1002tt = 23562 sq. ft. (3) CE=AF = AS=CP = 60 ft. (4) Area of the two quadrants CEP and AFS=^ of 602tt= sq. ft. 194 FAIRCHILDS SOLUTION BOOK. (5) HG = V( AH2). +2)=DL= FIG. The area included inDKGL has been grazedtwice, hence its area mustbe taken from the areaalready found. (6) DP=DS=20 ft. (7) HG = OD=40V2, (8) AH=|OD = HD= (9) AG=CG=60 ft.(10) (ID (12) V(+2)=DL = ft., side of square KL, and its area is = sq. ft. (13) The segments KSG and PLG are equal. (14) KS=LP=20 ft.— (15) Area of segments is (KS3-4-KGx4) +f of (KSx KGx2) = sq. ft. (16) Area grazed twice is + sq. ft. (17) .. The horse grazes over 23592+5654 88— sq. ft. PROBLEM stake to which a horse is tethered, is 120 ft. from, the corner of abarn 60 ft. long-, 40 ft. wide, and in line with the long- side of the barn:if the rope is 120 ft. long-, over how much ground can the horse graze? Solution. Let FCEA repre-sent the barn. O represents thepoint at which thehorse is tethered. OC = 20ft.,CE=40
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