Question

If Q is harmonic conjugate of 'P' with respect to A and B
and AP = 2; AQ = 6 then AB​

Answer 1

Given:

If Q is a harmonic conjugate of 'P' with respect to A and B and AP = 2; AQ = 6  

To find:

To find the value of AB

Solution:

From given, we have,

AP, AB and AQ are in HP.

AP = 2 and AQ = 6

we use the standard formula,

HP = 2ab/(a + b)

AB = (2 AP × AQ)/(AP + AQ)

substituting the given values in above equation, we get,

AB = (2 2 × 6)/(2 + 6)

AB = 2(12)/8

AB = 3

Therefore, the value of AB is 3.