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  • ABC IS RIGHT TRIANGLE ANGLE B IS 90 DEGERE . P AND Q ARE MP OF AB AND BC . PROVE THAT.1. 4PC SQUARE=4BC SQUARE + AB SQUARE 2. 4PC SQUARE + 4 AQ SQUARE= 5AC SQUARE

ABC IS RIGHT TRIANGLE ANGLE B IS 90 DEGERE . P AND Q ARE MP OF AB AND BC . PROVE THAT.1. 4PC SQUARE=4BC SQUARE + AB SQUARE 2. 4PC SQUARE + 4 AQ SQUARE= 5AC SQUARE

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1);4PC^2=4BC^2+AB^2\* In; riangle PBC,\* PC^2=PB^2+BC^2\* herefore PB=fracAB2\* LHS=4PC^2=PB^2+BC^2\*Rightarrow 4(PB^2+fracAB^24)=4BC^2+AB^2\*So,;4PC^2=4BC^2+AB^2\* 2);4PC^2+4AQ^2=5AC^2\* In; riangle PBC\* PC^2=BC^2+PB^2\* Rightarrow PC^2=BC^2+fracAB^24;;;;;(PB=fracAB2)\*In; riangle ABQ\*AQ^2= AB^2 +BQ^2\*Rightarrow AQ^2=AB^2+ fracBC^24;;;;;(BQ=fracBC2)\* Now,;LHS,\* 4PC^2+4AQ^2\* 4(BC^2+fracAB^24)+4(AB^2+fracBC^24)=5AB^2+5BC^2\* In; riangle ABC,\* Rightarrow AC^2=AB^2+BC^2\* Rightarrow 5(AB^2+BC^2)=5AC^2\*So,;4PC^2+4AQ^2=5AC^2

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Deependra Verma

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