Question

in a triangle ABC AB is greater than AC the bisector of Angle B and angle C meet at P prove that BP greater than CP​

Answer 1

Answer:

Step-by-step explanation:

Since BP is bisector ofbegin mathsize 12px style angle end styleABC, we have  begin mathsize 12px style fraction numerator A P over denominator P Q end fraction space equals space fraction numerator A B over denominator B Q end fraction space................... space left parenthesis 1 right parenthesis end style

Since CP is bisector ofbegin mathsize 12px style angle end styleACB, we have  begin mathsize 12px style fraction numerator A P over denominator P Q end fraction space equals space fraction numerator A C over denominator C Q end fraction space................... space left parenthesis space 2 right parenthesis space end style

Hence from (1) and (2),begin mathsize 12px style fraction numerator A P over denominator P Q end fraction space equals space fraction numerator A B plus A C over denominator B Q plus Q C end fraction space equals space fraction numerator A B plus A C over denominator B C end fraction end style