Question

In figure PA,QB,RC are each perpendicular to AC . Prove that 1/x +1/y= 1/z

Answer 1

From the figure we get the following equations by thales theorem z/x = QC/PC = BC/AC z/y = AC/AR = AB/AC Therefore z/x+z/y = (AB+BC)/AC = AC/AC = 1 =) z(1/x+1/y)=1 i.e. 1/x+1/y = 1/z