1) O is any point in the interior ofAABC Bisectors of ZAOB,E.BOC and A

1.	1) O is any point in the interior ofAABC Bisectors of ZAOB,E.BOC and AOC intersectside AB, side BC, side AC inF. D and E respectively.Prove thatob thot if it is
Answer» In ∆ AOB, OD is the bisector of angle AOB OA/OB =AD/DB---------------eq(1)Theorem used here [The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing angle] In ∆BOC .OE is the bisector of angle BOC OB/OC = BE/EC---------eq(2) In ∆COA, OF is the bisector of angle COA OC/OA =CF/FA-----------eq(3) Multiplying eq 1, 2, 3 (OA/OB) * (OB/OC) * (OC/OA) = (AD/DB) * (BE/EC) * (CF/FA) 1= (AD/DB) * (BE/EC) * (CF/FA) DBECFA = ADBECF ADBECF = DBECFA

1) O is any point in the interior ofAABC Bisectors of ZAOB,E.BOC and AOC intersectside AB, side BC, side AC inF. D and E respectively.Prove thatob thot if it is

Answer»

In ∆ AOB, OD is the bisector of angle AOB

OA/OB =AD/DB---------------eq(1)Theorem used here

[The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing angle]

In ∆BOC .OE is the bisector of angle BOC

OB/OC = BE/EC---------eq(2)

In ∆COA, OF is the bisector of angle COA

OC/OA =CF/FA-----------eq(3)

Multiplying eq 1, 2, 3

(OA/OB) * (OB/OC) * (OC/OA) = (AD/DB) * (BE/EC) * (CF/FA)

1= (AD/DB) * (BE/EC) * (CF/FA)

DB*EC*FA = AD*BE*CF

AD*BE*CF = DB*EC*FA