Question

In the adjoining figure,seg PA,seg QB, seg RC are perdendicular to seg AC . From information in figure, prove that, 1/x +1/z =1/y​

Answer 1

Answer:

Step-by-step explanation:

In ΔPAC and ΔQBC

∠PCA = ∠QCB

∠PAC = ∠QBC

ΔPAC congurent to ΔQBC

PA/QB = AC/BC

x/y = AB/BC  

y/x = BC/AC

In ΔRCA and ΔQBA

∠RAC = ∠QAB

∠RCA = ∠QBA

ΔRCA is congruent to ΔQBA

RC/QB = AC/AB

z/y= AC/AB

y/z= AB/AC

adding both eq

y/z + y/z = BC + AC/ AC = 1  

y/z + y/z = 1

multiplying both sides by y

1/x + 1/z = 1/y