A triangle has side lengths 4,6,8. A tangent is drawn to the incircle parallel to side 4cm cutting other two sides at M & N,then the length of MN is ? (A)10/9 (B)20/9 (C)5/3 (D)4/3

Asked by Anubhav Sachan | 21st Oct, 2013, 06:42: PM

Expert Answer:

Consider, the following figure,
Here triangle ABC is the given triangle with sides, a = 6, b = 4, c = 8
Ler r be the radius of the incircle.
Area of the triangle in terms of inradius is 
A = r × semi-perimeter of triangle
A = r × (a + b + c)/2 ....(i)
Area of triangle is given by
A = 1/2 bh ....(ii)
1/2 bh = r × (a + b + c)/2
 

Answered by Sneha shidid | 22nd Oct, 2013, 10:38: AM

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