CBSE Class 10 Answered
A triangle has side lengts 2,3,4. a tangent is drawn to the incircle parallel to side 2cm cutting the other two sides at M and N .Find the lenght MN.
let r be the radius of the in circle and a, b and c are the sides of the triangle ABC.
and XY || AC
area of the triangle ABC = 1/2 × bh and in terms of in circle radius.
area of triangle ABC = 1/2 × r × (a + b + c)
1/2 bh = 1/2 × r × (a + b + c)
r/h = b/(a + b + c) ....(i)
Triangles BXY and triangle BAC are similar triangles.
MQ/AC = (h - 2r)/h
= 1 - 2r/h
= 1 - 2b/(a + b + c)
= (a - b + c)/a + b + c) ....(ii)
Substitute AC = b = 2 , a = 3 and c = 4 in eq(ii):
MQ/2 = (3 - 2 + 4)/(2 + 3 + 4) = 5/9
MQ = 10/9