Find the incenter of the triangle formed by the following straight lin

1.	Find the incenter of the triangle formed by the following straight lines(i) x + 1 = 0, 3x - 4y = 5 and 5x + 12y = 27(ii) x + y - 7 = 0, x - y + 1 = 0 and x - 3y + 5 = 0
Answer» Step-by-step explanation: Let AB be x+y = 7 BC be x-y +1 = 0 AC be x-3y +5 = 0 A is 4 ,3 B is 3, 4 C is 1 ,2 AB = c = √2 AC = b = √10 BC = a = 2√2 16A^2 = 4108-( 2–10–8)^2 = 320–256 = 64 A = 2 Inradius = A/s = √2/ 3+√5

Find the incenter of the triangle formed by the following straight lines(i) x + 1 = 0, 3x - 4y = 5 and 5x + 12y = 27(ii) x + y - 7 = 0, x - y + 1 = 0 and x - 3y + 5 = 0

Answer»

Step-by-step explanation:

Let AB be x+y = 7

BC be x-y +1 = 0

AC be x-3y +5 = 0

A is 4 ,3

B is 3, 4

C is 1 ,2

AB = c = √2

AC = b = √10

BC = a = 2√2

16A^2 = 4*10*8-( 2–10–8)^2 = 320–256 = 64

A = 2

Inradius = A/s = √2/ 3+√5

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Find the incenter of the triangle formed by the following straight lines(i) x + 1 = 0, 3x - 4y = 5 and 5x + 12y = 27(ii) x + y - 7 = 0, x - y + 1 = 0 and x - 3y + 5 = 0​

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Find the incenter of the triangle formed by the following straight lines(i) x + 1 = 0, 3x - 4y = 5 and 5x + 12y = 27(ii) x + y - 7 = 0, x - y + 1 = 0 and x - 3y + 5 = 0