{"text_format":"1","workbook":"xlsx","n_sheets":8,"sheets":["Instructions","Dir-Dir","Dir-Dist","Dist-Dist","3-Point-Arc","3-Tangent-Arc","Tangent-Radius","Tangent-Dir"],"not_rendered":{"charts":0,"images":0,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Instructions","index":0,"n_rows":2,"n_cols":2,"rows_kept":2,"cut":false,"hidden":false,"merged":[]}
["COGO Intersections And Arcs Workbook"]
[null,"v1.0"]

{"sheet":"Dir-Dir","index":1,"n_rows":12,"n_cols":6,"rows_kept":12,"cut":false,"hidden":false,"merged":[]}
["Direction-Direction Intersection"]
[null,null,"Input:","Coodinates of two known points"]
[null,null,null,"Azimuth from each known point"]
[null,null,"Compute:","Coordinates of single intersection point"]
[]
[null,"Point","North","East","Azimuth","Dist"]
[null,"J",452.81,726.12,"330 19 10",{"$f":"((D8-D7)+(C7-C8)*TAN(RADIANS(dmstodeg(E8)))) / (SIN(RADIANS(dmstodeg(E7)))  -COS(RADIANS(dmstodeg(E7)))*TAN(RADIANS(dmstodeg(E8)))   )","v":401.8437897653543}]
[null,"K",742.2,731.5,"286 17 35",{"$f":"((C7-C8)+F7*COS(RADIANS(dmstodeg(E7))))/COS(RADIANS(dmstodeg(E8)))","v":212.90909696036135}]
[null,"diffs",{"$f":"C7-C8","v":-289.39000000000004},{"$f":"D7-D8","v":-5.3799999999999955}]
[]
[null,"Point","North","East"]
[null,"P",{"$f":"C7+Lat(E7,F7)","v":801.93172703047446},{"$f":"D7+Dep(E7,F7)","v":527.14148083714883}]

{"sheet":"Dir-Dist","index":2,"n_rows":15,"n_cols":8,"rows_kept":15,"cut":false,"hidden":false,"merged":[]}
["Direction-Distance Intersection"]
[null,null,"Input:","Coodinates of two known points"]
[null,null,null,"Azimuth from one known point"]
[null,null,null,"Distance from other known point"]
[null,null,"Compute:"," Coordinates of the two intersection points, P1 and P2"]
[]
[null,"Point","North","East","Azimuth"]
[null,"J",1419.51,3511.69,"329 46 45",null,"Quadratic solution coefficients"]
[null,null,"North","East","Distance",null,"a",1]
[null,"K",2056.64,2341.36,738.15,null,"b",{"$f":"2*C11*COS(RADIANS(dmstodeg((E8))))+2*D11*SIN(RADIANS(dmstodeg((E8))))","v":-2279.2118344263627}]
[null,"diffs",{"$f":"C8-C10","v":-637.12999999999988},{"$f":"D8-D10","v":1170.33},null,null,"c",{"$f":"C11^2+D11^2-E10^2","v":1230741.5232999995}]
[]
[null,"Point","Dist from J","North","East"]
[null,{"$f":"IF(C14>C15,\"P2\",\"P1\")","v":"P2"},{"$f":"(-H10+SQRT(H10^2-4*H9*H11))/(2*H9)","v":1400.2975420255193},{"$f":"$C$8+Lat($E$8,C14)","v":2629.4956818905148},{"$f":"$D$8+Dep($E$8,C14)","v":2806.8723953513522}]
[null,{"$f":"IF(C15>C14,\"P2\",\"P1\")","v":"P1"},{"$f":"(-H10-SQRT(H10^2-4*H9*H11))/(2*H9)","v":878.91429240084335},{"$f":"$C$8+Lat($E$8,C15)","v":2178.9726695378235},{"$f":"$D$8+Dep($E$8,C15)","v":3069.3024018861315}]

{"sheet":"Dist-Dist","index":3,"n_rows":14,"n_cols":7,"rows_kept":14,"cut":false,"hidden":false,"merged":[]}
["Distance-Distance Intersection"]
[null,null,"Input:","Coordinates of two known points."]
[null,null,null,"Distance from each known point."]
[null,null,"Compute:","Coordinates of the two intersection points, P1 and P2"]
[]
[null,"Point","North","East","Radius"]
[null,"J",4593.1000000000004,1645.48,559.83000000000004]
[null,"K",4942.5600000000004,1014.02,374.91]
[null,"diffs",{"$f":"C8-C7","v":349.46000000000004},{"$f":"D8-D7","v":-631.46}]
[null,null,null,null,null,"Quadratic coefficients"]
[null,"Point","North","East",null,"K",{"$f":"C7^2-C8^2+D7^2-D8^2+E8^2-E7^2","v":-1825815.9943999997}]
[null,"P1",{"$f":"((D12*2*D9)+G11)/(-2*C9)","v":4574.6159406494253},{"$f":"(-G13-SQRT(G13^2-4*G12*G14))/(2*G12)","v":1085.9552298155841},null,"a",{"$f":"1+D9^2/C9^2","v":4.2651019431083128}]
[null,"P2",{"$f":"((D13*2*D9)+G11)/(-2*C9)","v":5077.0146379358684},{"$f":"(-G13+SQRT(G13^2-4*G12*G14))/(2*G12)","v":1363.9906536804688},null,"b",{"$f":"(2*D9*C7/C9)-(2*D7)+(D9*G11/C9^2)","v":-10449.268948209226}]
[null,null,null,null,null,"c",{"$f":"(G11*C7/C9)+(G11^2/(4*C9^2))+C7^2+D7^2-E7^2","v":6317608.8243123703}]

{"sheet":"3-Point-Arc","index":4,"n_rows":13,"n_cols":7,"rows_kept":13,"cut":false,"hidden":false,"merged":[]}
["Three-point Arc"]
[null,null,"Input:","Coordinates of three non-linear points"]
[null,null,"Compute:","Circle radius, R"]
[null,null,null,"Coordinates of radius point, O"]
[]
[null,"Point","North","East",null,"Solution coefficients"]
[null,"J",902.72,1751.91,null,"A",{"$f":"(D8^2-D9^2+C8^2-C9^2)/(D8-D9)","v":-5919.7177743682132}]
[null,"K",870.76,1237.76,null,"B",{"$f":"(D7^2-D9^2+C7^2-C9^2)/(D7-D9)","v":4189.1479367847405}]
[null,"L",538.57000000000005,1293.1600000000001,null,"C",{"$f":"2*(C8-C9)/(D8-D9)","v":-11.992418772563155}]
[null,null,null,null,null,"D",{"$f":"2*(C7-C9)/(D7-D9)","v":1.5875749318801089}]
[]
[null,"Radius Pt","North","East","Radius"]
[null,"O",{"$f":"(G7-G8)/(G9-G10)","v":744.39399098141075},{"$f":"(D7^2-D9^2+C7^2-C9^2-2*C13*(C7-C9))/(2*(D7-D9))","v":1503.6833486302328},{"$f":"SQRT(($C$7-C13)^2+($D$7-D13)^2)","v":294.420779806729}]

{"sheet":"3-Tangent-Arc","index":5,"n_rows":20,"n_cols":8,"rows_kept":20,"cut":false,"hidden":false,"merged":[[11,6,11,7]]}
["Three-Tangent Arc"]
[null,null,"Input:","Coordinates of three known points"]
[null,null,null,"Azimuth from each point"]
[null,null,"Compute:","Radius of tangent arc"]
[null,null,null,"Coordinates of radius point, O"]
[]
[null,"Point","North","East","Azimuth","dN","dE"]
[null,"A",1513.48,978.2,"44 12 02"]
[null,"B",1904.46,1129.07,"107 17 05",{"$f":"C9-C8","v":390.98},{"$f":"D9-D8","v":150.86999999999989}]
[null,"C",1902.29,1598.02,"156 20 45",{"$f":"C10-C9","v":-2.1700000000000728},{"$f":"D10-D9","v":468.95000000000005}]
[]
[null,"Line intersections",null,null,null,null,"Arc data"]
[null,"PI",null,"dist","North","East","Delta","Tan dist"]
[null,"G","from A",{"$f":"((D9-D8)+(C8-C9)*TAN(RADIANS(dmstodeg(E9)))) / (SIN(RADIANS(dmstodeg(E8))) - COS(RADIANS(dmstodeg(E8)))*TAN(RADIANS(dmstodeg(E9)))   )","v":468.95011124025319},{"$f":"C8+Lat(E8,D14)","v":1849.6721391336634},{"$f":"D8+Dep(E8,D14)","v":1305.1389123628103},{"$f":"degtodms(dmstodeg(E9)-dmstodeg(E8))","v":"63 05 03"},{"$f":"E20*TAN(RADIANS(dmstodeg(G14))/2)","v":219.72120384515796}]
[null,"H","from B",{"$f":"((D10-D9)+(C9-C10)*TAN(RADIANS(dmstodeg(E10)))) / (SIN(RADIANS(dmstodeg(E9))) - COS(RADIANS(dmstodeg(E9)))*TAN(RADIANS(dmstodeg(E10)))   )","v":567.48071739888678},{"$f":"C9+Lat(E9,D15)","v":1735.8499709731143},{"$f":"D9+Dep(E9,D15)","v":1670.9233221556437},{"$f":"degtodms(dmstodeg(E10)-dmstodeg(E9))","v":"49 03 40"},{"$f":"E20*TAN(RADIANS(dmstodeg(G15))/2)","v":163.36327823713663}]
[null,null,null,"diff",{"$f":"E15-E14","v":-113.82216816054915},{"$f":"F15-F14","v":365.78440979283346}]
[null,"dGH",{"$f":"SQRT(E16^2+F16^2)","v":383.08448208229458},"AzJO",{"$f":"degtodms(dmstodeg(E9)+SIGN(E20)*90)","v":"197 17 05"}]
[]
[null,"Radius Pt","North","East","Radius","Curve to"]
[null,"O",{"$f":"E14+Lat(E9,H14)+Lat(E17,ABS(E20))","v":1442.5920694071533},{"$f":"F14+Dep(E9,H14)+Dep(E17,ABS(E20))","v":1408.5797546002671},{"$f":"C17/( TAN(RADIANS(dmstodeg(G14))/2  )+TAN(RADIANS(dmstodeg(G15))/2  ))","v":357.96198623899892},{"$f":"IF(E20<0,\"Left\",\"Right\")","v":"Right"}]

{"sheet":"Tangent-Radius","index":6,"n_rows":16,"n_cols":6,"rows_kept":16,"cut":false,"hidden":false,"merged":[]}
["Tangent Radius"]
[null,null,"Input:","Coordinates of known point"]
[null,null,null,"Azimuth from known point"]
[null,null,null,"Coordinates of radius point, O"]
[null,null,"Compute:","Radius of tangent arc"]
[]
[null,null,null,"North","East","Az to P"]
[null,"Point","Q",2200.94,1510.91,"134 25 45"]
[null,"Radius point","O",2090.4299999999998,1754.2,{"$f":"degtodms(dmstodeg(F8)+90)","v":"224 25 45"}]
[null,null,"diffs",{"$f":"D9-D8","v":-110.51000000000022},{"$f":"E9-E8","v":243.28999999999996}]
[]
[null,"Line QO","dQO",{"$f":"SQRT(D10^2+E10^2)","v":267.21243271973714},"AzQO",{"$f":"InverseAz(D10,E10)","v":"114 25 44.57"}]
[null,"Triangle QOP","Angle Q",{"$f":"degtodms(ABS(dmstodeg(F8)-dmstodeg(F12)))","v":"20 00 0.43"},"dQP",{"$f":"D12*COS(RADIANS(dmstodeg(D13)))","v":251.097360683575}]
[]
[null,null,"Point","North","East","Radius"]
[null,null,"P",{"$f":"D8+Lat(F8,F13)","v":2025.165079121854},{"$f":"E8+Dep(F8,F13)","v":1690.2227483826482},{"$f":"D12*SIN(RADIANS(dmstodeg(D13)))","v":91.392557999777424}]

{"sheet":"Tangent-Dir","index":7,"n_rows":17,"n_cols":7,"rows_kept":17,"cut":false,"hidden":false,"merged":[]}
["Tangent-Direction"]
[null,null,"Input:","Coordinates of known point"]
[null,null,null,"Coordinates of arc center"]
[null,null,null,"Arc radius"]
[null,null,"Compute:","Direction to and coordinates of two tangent points, P1 and P2"]
[]
[null,null,null,"North","East","Radius"]
[null,"Point","Q",1325.15,1243.5999999999999]
[null,"Radius pt","O",1023.46,1958.51,500]
[]
[null,null,null,"dN","dE","Dist","Azimuth"]
[null,null,"Line QO",{"$f":"D9-D8","v":-301.69000000000005},{"$f":"E9-E8","v":714.91000000000008},{"$f":"SQRT(D12^2+E12^2)","v":775.95951195922601},{"$f":"InverseAz(D12,E12)","v":"112 52 46.58"}]
[null,null,"angle g",{"$f":"degtodms(DEGREES(ASIN(F9/F12)))","v":"40 07 04.69"}]
[]
[null,null,"Point","N","E","dQP","AzQP"]
[null,null,"P1",{"$f":"D8+Lat(G16,F16)","v":796.44593576268767},{"$f":"E8+Dep(G16,F16)","v":1513.0163630126203},{"$f":"SQRT(F12^2-F9^2)","v":593.39124041394496},{"$f":"degtodms(dmstodeg(G12)+dmstodeg(D13))","v":"152 59 51.27"}]
[null,null,"P2",{"$f":"D8+Lat(G17,F17)","v":1501.000106536628},{"$f":"E8+Dep(G17,F17)","v":1810.3361857434697},{"$f":"F16","v":593.39124041394496},{"$f":"degtodms(dmstodeg(G12)-dmstodeg(D13))","v":"72 45 41.88"}]