ch circles

Asked by nilesh.dhote74 | 15th Dec, 2020, 07:21: PM

Expert Answer:

Question: If n = 2pab/a+b, using properties of proportion, find value of n+pa/n-pa + n+pb/n-pb.
Solution:
As space straight n equals fraction numerator 2 pab over denominator straight a plus straight b end fraction
rightwards double arrow straight n over pa equals fraction numerator 2 straight b over denominator straight a plus straight b end fraction
rightwards double arrow fraction numerator straight n plus pa over denominator straight n minus pa end fraction equals fraction numerator 2 straight b plus straight a plus straight b over denominator 2 straight b minus straight a minus straight b end fraction space space space space space... space left parenthesis Componendo space and space dividendo right parenthesis
rightwards double arrow fraction numerator straight n plus pa over denominator straight n minus pa end fraction equals fraction numerator 3 straight b plus straight a over denominator straight b minus straight a end fraction space space space space... space left parenthesis straight i right parenthesis
Again space as space straight n equals fraction numerator 2 pab over denominator straight a plus straight b end fraction
rightwards double arrow straight n over pb equals fraction numerator 2 straight a over denominator straight a plus straight b end fraction
rightwards double arrow fraction numerator straight n plus pb over denominator straight n minus pb end fraction equals fraction numerator 2 straight a plus straight a plus straight b over denominator 2 straight a minus straight a minus straight b end fraction space space space space space... space left parenthesis Componendo space and space dividendo right parenthesis
rightwards double arrow fraction numerator straight n plus pb over denominator straight n minus pb end fraction equals fraction numerator 3 straight a plus straight b over denominator straight a minus straight b end fraction space space space space... space left parenthesis ii right parenthesis
Adding space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space get
fraction numerator straight n plus pa over denominator straight n minus pa end fraction plus fraction numerator straight n plus pb over denominator straight n minus pb end fraction equals fraction numerator 3 straight b plus straight a over denominator straight b minus straight a end fraction plus fraction numerator 3 straight a plus straight b over denominator straight a minus straight b end fraction
equals negative fraction numerator 3 straight b plus straight a over denominator straight a minus straight b end fraction plus fraction numerator 3 straight a plus straight b over denominator straight a minus straight b end fraction
equals fraction numerator negative 3 straight b minus straight a plus 3 straight a plus straight b over denominator straight a minus straight b end fraction
equals fraction numerator negative 2 straight b plus 2 straight a over denominator straight a minus straight b end fraction
equals fraction numerator 2 open parentheses straight a minus straight b close parentheses over denominator straight a minus straight b end fraction
equals 2

Answered by Renu Varma | 17th Dec, 2020, 10:59: AM