Calculating 2R, diameter of the red inscribed circle.a = ½(16)a = 8 units.a is the radius of the inscribed yellow half circle.b = (16-R) units.c²+R² = b²c² = (16-R)²-R²c = √(256-32R+R²-R²)c = √(256-3...
Calculating the area of the semi circle.Let r be the radius of the half circle.a = 2r units.a is the diameter of the half circle.b² = (2r)²+7²-2*7*2rcosxb² = 4r²+49-28rcosx --- (1).b² = 2(15)²+2(15)²...
Calculating x.Let a be each of the two equal lengths.b² = 2a²b = √(2a²)b = √(2)a units.c = 2√(2)+5√(2)c = 7√(2) units.It implies;a ~ b7√(2) ~ dTherefore;a ~ √(2)a7√(2) ~ dCross Multiply.ad = 14ad = 1...
Calculating length CD.a = 360-60-60-90a = 150°a is angle BCD.b = 180-ab = 180-150b = 30°sin30 = c/x½ = c/xc = ½(x) units.d = x+xd = 2x units.d is AB.e = c+x+10e = ½(x)+x+10e = ½(3x+20) units.e = d.It...
Calculating Area Blue, Inscribed Square Area.Notice.2 units is the radius of the inscribed circle.tan60 = 2/a√(3) = 2/aa = ⅓(2√(3)) units.a = 1.15470053838 units.sin60 = 2/b½√(3) = 2/b4 = √(3)bb = ⅓(...
Calculating length PD, let it be x.Notice.At the inscribed triangle.AB should be 4 cm.While AC should be 6 cm.Resolving with the above corrections.5² = 6²+4²-2*6*4cosa48cosa = 52-25a = acos(27/48)a =...
Calculating angle QRS.Let it be x.a = 45-32a = 23°a is ang SPQ.b = 90-ab = 90-23b = 67°b is angle PQS.c = b-45c = 67-45c = 22°c is angle RQS.d = 180-45d = 135°d is angle QSR.It implies, thec- require...
Calculating x/y.Let the side length of the congruent squares be 1 unit each.x² = 1²+1²x² = 2x = √(2) units.a = 1+1+1a = 3 units.b² = 1²+a²b² = 1²+3²b = √(10) units.b is the radius of the circle.Andb...
Calculating area x.Let 3a be the height of the ascribed triangle.Therefore, considering the 6 square units inscribed triangle area.½*(3a)*b = 63ab = 12b = (4/a) units.b is the base of the 6 square un...
Calculating Alpha.Let it be x.Let 1 unit be the side length of the inscribed square.Let r be the radius of the ascribed quarter circle.a² = 1²+1²a =√(2) units.a is OE, the diameter of the inscribed...
