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Secondary School Math 8 points

In the given figure, PA, QB and RC are perpendicular to AC. prove that 1/x + 1/y = 1/z

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sharinkhan Expert

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

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