Question

D , E and F are the points on sides BC , CA and AB respectively of △ABC . Such that AD bisects ∠A , BE bisects ∠B and CF bisects ∠C . If AB = 5cm , BC = 8cm and CA = 4cm , determine AF , CE and BD ...Draw the fig also

Answer 1

your answer.... confirm the answer in comment.

Answer 2

Figure:-

Given:-

• D , E and F are the points on sides BC , CA and AB respectively of △ABC .
• AB = 5cm , BC = 8cm and CA = 4cm

To find:-

• Find the value AF , CE and BD ...?

Solutions:-

• AB = 5cm, BC = 8cm and CA = 4cm

Since AD bisector of <A

So AB/AC = BD/CD

Then,

=> 5/4 = BD/ BC - BD

=> 5/4 = BD/8 - BD

=> 40 - 5BD = 4BD

=> 9BD = 40

So, BD = 40/9 cm.

Since BE is the bisector of <B.

=> AB/BC = AE/EC

=> AB/BC = AC - EC/EC

=> 5/8 = 4 - CE/CE

=> 5CE = 32 - 8CE

=> 5CE + 8CE = 32

=> 13CE = 32

So, CE = 32/13 cm.

Now since CF is the bisector of <C

So BC/CA = BF/AF

=> 8/4 = AB - AF/AF

=> 8/4 = 5 - AF /AF

=> 8AF = 20 - 4AF

=> 12AF = 20

So 3AF = 5

=> AF = 5/3 cm

Hence, the BD = 40/9, CE = 32/13 cm and AF = 5/3 cm.