ABC is a triangle in which AB=AC and I is the incentre of triangle
given BC=AB+AI find angle BAC
ABC is a triangle in which AB=AC and I is the incentre of triangle
given BC=AB+AI find angle BAC
pankaj jindal , 16 Years ago
Grade 11
Analytical Geometry> MATHS...
2 AnswersSaurabh Koranglekar
Vikas TU
ΔABC is isosceles as AB=AC,
In ΔABD: cosB = a/2b ----- (1)
In ΔAIE: r = AI sin A/2 = AI cosB = AI *a/2b using (1) ...... (2)
In ΔBID: r = a/2 * tan(B/2)
=> AI = 2br /a = b tan(B/2) using (2) ...... (3)
In ΔAIE: r = AI sin A/2 = AI cosB = AI *a/2b using (1) ...... (2)
In ΔBID: r = a/2 * tan(B/2)
=> AI = 2br /a = b tan(B/2) using (2) ...... (3)
given a = b + AI = b [1+tan(B/2) ] using (3)
from (1) & (2): 1+ tan(B/2)] = 2*CosB = [1 - tan²(B/2)]/[1+tan²(B/2)]
=> tan^2 B/2 + 2 tan B/2 - 1 = 0
=> tan B/2 = √2 - 1=> cosB = 1/√2
B = 45 = C
A = 90
=> tan B/2 = √2 - 1=> cosB = 1/√2
B = 45 = C
A = 90
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