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In the given figure, seg PA, seg QB andseg RC are perpendicular to seg AC.From the information given prove that 1/x + 1/z= 1/y |
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Answer» Step-by-step explanation: Consider △CAP and △CBQ ∠CAP=∠CBQ=90 ∘
∠PCA=∠QCB (common angle) So by AA, △CAP∼△CBQ Hence AP BQ
= AC BC
x y
= AC BC
(1) Now consider △ACR and △ABQ ∠ACR=∠ABQ=90 ∘
∠QAB=∠RAC (common angle) So by AA, △ACR∼△ABQ Hence CR BQ
= AC AB
z y
= AC AB
(2) Adding (1) and (2) x y
+ z y
= AC BC
+ AC AB
y( x 1
+ z 1
)= AC BC+AB
y( x 1
+ z 1
)= AC AC
y( x 1
+ z 1
)=1 x 1
+ z 1
= y 1
Hence proved. helpful to you |
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