In the adjoining figure, sides BC, CA and AB of ABCTouch a circle a

1.	In the adjoining figure, sides BC, CA and AB of ABCTouch a circle at point D, E and F respectively.If BD = 4 cm, DC = 3 cm and CA = 8 cm, then the length ofSide AB is:
Answer» Given :- ∆ABC is a ∆. Circle Touches sides BC, CA and AB of ∆ABC Touch a circle at point D, E and F respectively. BD = 4cm. DC = 3CM. CA = 8cm. To Find :- Side AB ? . Solution :- Refer to Image First. Tangent Theoram :- States that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same. So, with Tangent Theoram we get :- → AF = AE → DC = CE → BD = BF . so, → BD = 4cm. (Given). → BF = 4cm. --------------- Equation (1). And, → DC = 3cm. (Given). So, → CE = 3cm. So, → AE = CA - CE → AE = 8 - 3 → AE = 5cm. So, → AF also = 5cm. ------------ Equation (2). Hence, From Equation (1) & (2), we get, → AB = AF + FB → AB = 5 + 4 → AB = 9cm. (Ans).

In the adjoining figure, sides BC, CA and AB of ABCTouch a circle at point D, E and F respectively.If BD = 4 cm, DC = 3 cm and CA = 8 cm, then the length ofSide AB is:

Answer»

Given :-

∆ABC is a ∆.
Circle Touches sides BC, CA and AB of ∆ABC
Touch a circle at point D, E and F respectively.
BD = 4cm.
DC = 3CM.
CA = 8cm.

To Find :-

Side AB ? .

Solution :-

Refer to Image First.

Tangent Theoram :- States that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same.

So, with Tangent Theoram we get :-

→ AF = AE

→ DC = CE

→ BD = BF .

so,

→ BD = 4cm. (Given).

→ BF = 4cm. --------------- Equation (1).

And,

→ DC = 3cm. (Given).

So,

→ CE = 3cm.

So,

→ AE = CA - CE

→ AE = 8 - 3

→ AE = 5cm.

So,

→ AF also = 5cm. ------------ Equation (2).

Hence, From Equation (1) & (2), we get,

→ AB = AF + FB

→ AB = 5 + 4