In the given figure PA, OB and RC each isperpendicular to AC such that

1.	In the given figure PA, OB and RC each isperpendicular to AC such that PA = x,RC-y, QB-z, AB-a and BC = b.Prove that+[CBSE 2015]
Answer» InΔPAC andΔQBC∠PCA =∠QCB∠PAC =∠QBC ΔPAC congurent toΔQBCPA/QB = AC/BCx/y = AB/BCy/x = BC/AC InΔRCA andΔQBA∠RAC =∠QAB∠RCA =∠QBAΔRCA is congruent toΔQBARC/QB = AC/AB z/y= AC/ABy/z= AB/AC adding both eqy/z + y/z = BC + AC/ AC = 1 y/z + y/z = 1 multiplying both sides by y 1/x + 1/z = 1/y

In the given figure PA, OB and RC each isperpendicular to AC such that PA = x,RC-y, QB-z, AB-a and BC = b.Prove that+[CBSE 2015]

Answer»

InΔPAC andΔQBC∠PCA =∠QCB∠PAC =∠QBC

ΔPAC congurent toΔQBCPA/QB = AC/BCx/y = AB/BCy/x = BC/AC

InΔRCA andΔQBA∠RAC =∠QAB∠RCA =∠QBAΔRCA is congruent toΔQBARC/QB = AC/AB

z/y= AC/ABy/z= AB/AC

adding both eqy/z + y/z = BC + AC/ AC = 1

y/z + y/z = 1

multiplying both sides by y

1/x + 1/z = 1/y