Question

A circle is inscribed in a triangle abc where ab =8cm

Answer 1

 Tangents drawn from an external point to a circle are equal. 
⇒ AD = AF, BD = BE,
CE = CF.
 Let AD = AF = a  
BD = BE = b  
CE = CF = c   
AB = AD + DB = a + b = 8 -------- (1) 
BC = BE + EC = b + c = 10 -------- (2) 
AC = AF + FC = a + b = 12 -------- (3)   
Adding (1), (2) and (3), we get 
2 (a + b + c) = 30 ⇒ (a + b + c) = 15 -------- (4)   
Subtracting (1) from (4), we get c = 7 
Subtracting (2) from (4), we get a = 5 
Subtracting (3) from (4), we get b = 3   
Therefore,
AD = a = 5 cm,
BE = b = 3 cm,
CF = c = 7 cm