Question

if a circle of 4cm is inscriebed in a triangle of the sides, 8+x, 6+x and 8+6. then find the value of x....
please help fast

Answer 1

the value of x is 4 after taking logic

Answer 2

area of triangle ABC
s=8+8+6+6+x+x/2
28+2x/2
=14+ x
(s-a)= 14-x ---(8+x)
=6
(s-b)= 14-x----(6+x)
=8
(s-c)=14+x ----- (14)
=x
A=✓14+x*(6)*(8)*(x)
= ✓l4+x *48x. -----(1)
area of triangle AOB
1/2*8+X*4
=16+X----2
area of triangle BOC
1/2*14*4
=28----3
area of triangle AOC
1/2*6+x*4
=12+x---(4)
add in 2+3+4
16+2x+12+2x+28=56+4x---6
equating eq 1 and 6
✓14+x*48x =4(14+x)
sq on both sides
48x(14+x)= 4square (14+x) square
48x(14+x)= 16(14+x)(14+x)
48x*3x=x+14
2x= 14
x= 7
6+7= 13
8+7 =15