Q. 63.6( 38 Votes )

AB, CD, PQ are perpendicular to BD. AB = x, CD = y and PQ = z prove that 1/x + 1/y = 1/z


Answer :

Given, in Δ BCD, PQ || CD


….eq(1)


And in Δ ABD, PQ||AB


….eq(2)


Need to prove that


From eq(1) and eq(2) we have



1- [FROM EQ(1)]


1 = PQ()


…..eq(3)


Since, from the question we know that AB = X CD = Y and PQ = z


Substituting those values in eq(3) we get




Hence proved


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