Question

BO and CO are respectively bisector of angle B and angle C of triangle ABC . AO produce meets BC at P . then find AB/AC​

Answer 1

SOLUTION

Given, BO and CO are the bisector of <B and <C of triangle ABC. AO is produce to meet BC at point P.

To prove: (i) AB/BP=AO/OP

(ii) AC/CP=AO/OP

(iii) AB/AC=BP/CP

(iv) AP is the bisector of <BAC

Proof: i) In triangle ABP, BO is the bisector of <B

therefore, AB/BP=AO/OP ------(1)

ii) In triangle ACP, OC is the bisector of <C

therefore, AC/CP=AO/OP -------(2)

iii) From equation (1) and (2),

AB/BP=AC/CP

=>AB/AC=BP/CP ------(3)

iv) In triangle ABC,

AB/AC=BP/CP (From 3)

therefore, AP is the bisector of <BAC.