Question

D,E and F are the points on sites BC,CA and AB respectively of triangle ABC such that AD bisects angle A, and BE bisects angle B and CF bisect angle C . if AB = 5cm, BC = 8cm and CA = 4cm, determine AF,CE and BD.

Answer 1

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given in question ,

AB = 5 cm

BC = 8 cm

CA = 4 cm

in question ,

solving , AF = ?

CE =?

BD = ?

AD is the bisector of angle A .

so,

AB / AC = BD / CD

again,

54 = BD . CD - BD

=> 54 = 8 BD - BD = 40 - 5BD = 4 BD => 9BD = 40

SO,

BD = 40 / 9

BE IS THE BISECTOR OF ANGLE A .

ABBC = AEEC = ABBC = AC - ECEC.

5/ 8 = 4 - CE / CE

5CE = 32 - 8CE

5CE + 8CE = 32

SO,

CE = 32 / 13 CM

NOW , SINCE CF IS THE BISECTOR OF ANGLE C.

SO,

BC / CA = BE / AF

8 / 4 = AB - AF / AF

8 / 4 = 5 - AF / AF

8 AF = 20 - 4AF

12AF = 20

SO ,

3AF = 5 CM

AF = 5 / 3 CM

NEXT ,

CE = 32 / 13 CM

OR ,

BD = 40 / 9 CM

BE BRAINLY.

Answer 2

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