+44 n triangle ABC, AB=13, AC=14 and BC=15. Let I be the incenter. The incircle of triangle ABC touches sides BC, AB, and AC at D, E, and F, respectively. Find the area of quadrilateral AEIF.
+12527 An triangle ABC, AB=13, AC=14 and BC=15. Let I be the incenter. The incircle of triangle ABC touches sides BC, AB, and AC at D, E, and F, respectively. Find the area of quadrilateral AEIF.
+1486 In triangle ABC, AB=13, AC=14 and BC=15. Let I be the incenter. The incircle of triangle ABC touches sides BC, AB, and AC at D, E, and F, respectively. Find the area of quadrilateral AEIF.
AB = 13 AC = 14 BC = 15
I c I I b I I a I
Semiperimeter s = ( a + b + c )/2 = 21
Triangle (ABC) area is: A = sqrt [ s (s-a)(s-b)(s-c)] = 84 u²
Radius r = A / s = 4
Angle BAC => cos(∠A) = ( b² + c² - a² ) / 2bc = 67.38°
AE = AF = r / tan (∠A/2) = 6
Area of quadrilateral AEIF = AF * r = 24 u² 
