+0

# triangle

0
141
3

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.

Mar 11, 2020

#1
-1

deleted

Mar 11, 2020
edited by Melody  Mar 11, 2020
#2
+2

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.    Mar 11, 2020
#3
+2

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 Mar 12, 2020
edited by Dragan  Mar 12, 2020
edited by Dragan  Mar 12, 2020
edited by Dragan  Mar 16, 2020