Question

In fig.7.143,PA,QB and RC are perpendicular to AC. Prove that 1/x+1/z=1/y.
Help me guys!!!!​

Answer 1

Answer:

given:PA ,QB and RC are perpendicular to AC

let AB=a and BC=b

in triangle QCB and triangle CPA,

angle QCB= angle PCA (common)

angle QBC=angle PAC=90°

therefore, triangle QCB is similar to triangle CPA(AA similarity)

therefore, QB/PA=CB/CA

y/x=b/a+b....1

in triangle AQB and triangle ARC

angle QAB= angle RAC (common)

angle ABQ=angle ACR=90°

therefore, triangle AQB is similar to triangle ARC

(by AA similarity)

therefore, QB/RC=AB/AC

y/z=a/a+b.....2

from 1 and 2

y/x+y/z=b/a+b +a/a+b

y(1/x + 1/z)=b+a/a+b

y(1/x + 1/z)=1

therefore, 1/x +1/z=1/y