Question

In the given figure, a circle inscribed in a triangle ABC touches the sides AB, BC and CA at points D, E and F respectively. If AB = 14 cm, BC = 8 cm and CA = 12 cm. Find the lengths AD, BE and CF.

Answer 1

We know that tangent segments to a circle from the same external point are congruent
Now, we nave
AD = AF,BD = BE and CE = CF
Now AD + BD = 14cm           …..(1)
AF + FC = 12cm
⇒ AD + FC = 12cm              .........(2)
BE + EC = 8cm
⇒ BD + FC= 8 cm               ...........(3)
Adding all these we get
AD + BD + AD +FC +BD+ FC = 342
⇒ 2(AD + BD + FC) = 34 
⇒ AD+ BO+ FC = 17cm          ............(4)
Solving (1) and (4), we get
FC = 3cm
Solving (2) and (4), we get

BD = 5cm = BE
Solving (3) and (4), we get
and AD =  9cm