Triangle ABC is right angled at C.P and Q divide AC and BC in 2:3.Prove that
I) 25BP2=9AC2+25BC2
II)  25AQ2=25AC2+9BC2
III) 25 (AQ2+BP2)=34AB2

Asked by Chelsea Dhawan | 11th Oct, 2014, 08:02: PM

Expert Answer:

A P equals 2 over 5 A C left parenthesis i right parenthesis space 25 B P squared equals 9 A C squared plus 25 B C squared L H S comma equals 25 B P squared equals 25 left parenthesis B C squared plus C P squared right parenthesis equals 25 B C squared plus 25 C P squared equals 25 B C squared plus 25 left parenthesis A C minus A P right parenthesis squared equals 25 B C squared plus 25 open parentheses A C minus 2 over 5 A C close parentheses squared equals 25 B C squared plus 25 open parentheses 3 over 5 A C close parentheses squared equals 25 B C squared plus 25 cross times 9 over 25 A C squared equals 9 A C squared plus 25 B C squared
left parenthesis i i right parenthesis C Q equals 3 over 5 B C 25 A Q squared equals 25 A C squared plus 9 B C squared L H S comma 25 A Q squared equals 25 left parenthesis A C squared plus C Q squared right parenthesis equals 25 A C squared plus 25 C Q squared equals 25 A C squared plus 25 space open parentheses 3 over 5 B C close parentheses squared equals 25 A C squared plus 9 over 25 B C squared equals 25 A C squared plus 9 B C squared equals R H S
 
25 open parentheses A Q squared plus B P squared close parentheses equals 34 A B squared L H S equals 25 open parentheses A Q squared plus B P squared close parentheses equals 25 left parenthesis A C squared plus C Q squared right parenthesis plus 25 left parenthesis C P squared plus B C squared right parenthesis equals 25 A C squared plus 25 open parentheses 3 over 5 B C close parentheses squared plus 25 open parentheses 3 over 5 A C close parentheses squared plus 25 B C squared equals 25 A C squared plus 25 9 over 25 B C squared plus 25 9 over 25 A C squared plus 25 B C squared equals 34 A C squared plus 34 B C squared equals 34 left parenthesis A C squared plus B C squared right parenthesis equals 34 A B squared equals R H S

Answered by Prasenjit Paul | 13th Oct, 2014, 10:42: AM