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CBSE Class 10 Answered

Please help to solve the question. 
question image
Asked by adilaman.java | 08 Feb, 2019, 06:00: PM
answered-by-expert Expert Answer
PQ divide the triangle into two half of equal area.
 
Hence, begin mathsize 12px style 1 half cross times P Q cross times A R space equals space 1 half cross times left parenthesis P Q plus B C right parenthesis cross times R D end style
begin mathsize 12px style fraction numerator R D over denominator A R end fraction equals space fraction numerator P Q over denominator P Q plus B C end fraction space space space o r space space space space fraction numerator begin display style R D end style over denominator begin display style A R end style end fraction plus 1 equals space fraction numerator A D over denominator A R end fraction space equals space fraction numerator begin display style P Q end style over denominator begin display style P Q plus B C end style end fraction plus 1 space end style ................................(1)
ΔAPQ and ΔABC are similar triangles. Hence begin mathsize 12px style fraction numerator A D over denominator A R end fraction equals fraction numerator A B over denominator A P end fraction end style............................(2)
from (1) and (2) , begin mathsize 12px style fraction numerator A B over denominator A P end fraction equals space fraction numerator P Q over denominator P Q plus B C end fraction plus 1 end style
begin mathsize 12px style fraction numerator A B over denominator A P end fraction minus 1 space equals space fraction numerator A B minus A P over denominator A P end fraction space equals space fraction numerator B P over denominator A P end fraction space equals space fraction numerator P Q over denominator P Q plus B C end fraction end style
Hence begin mathsize 12px style fraction numerator A P over denominator B P end fraction equals fraction numerator P Q plus B C over denominator P Q end fraction space equals space 1 plus fraction numerator B C over denominator P Q end fraction end style
Answered by Thiyagarajan K | 09 Feb, 2019, 11:02: PM

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