#hat A = pi/12, hat B = (5pi)/8, hat C = (7pi) / 24, A_t = 13#
#A_t = (1/2) a b sin C = (1/2) bc sin A = (1/2) ca sin B#
#ab = (2 A_t) / sin C = 26 / sin ((7pi)/24) = 32.77#
#bc = A_t / sin A = 26/ sin (pi/12) = 100.46#
#ca = A_t / sin C = 26 / sin(5pi)/8) = 28.14#
#a = (abc) / (bc) = sqrt(32.77 * 100.46 * 28.1) / 100.46 = 3.03#
#b = (abc) / (ac) = sqrt(32.77 * 100.46 * 28.1) / 28.14 =10.81#
#c = (abc) / (ab) = sqrt(32.77 * 100.46 * 28.1) / 32.77 = 9.28#
#"Semiperimeter " = s = (a + b + c) / 2 = (3.03 + 10.81 + 9.28) / 2 = 11.56#
#"Incircle radius " = r = A_t / s = 13 / 23.12#
#color(purple)("Area of incircle " = A_i = pi * (13/23.12)^2 = 0.9933 " sq units"#