Question

5. If P divides OA internally in the ratio x1 : x2 and divides OA externally in the ratio x1 : x2 ,then prove that OA is the
harmonic mean of OP and 0Q​

Answer 1

The required expression 1/OP+1/OQ= 2/OA

Step-by-step explanation:

Given: P divides OA internally in the ratio x1 : x2 and Q divides OA externally in the ratio x1 : x2

To find relation between OA,OP,OQ

Solution: According to the condition

1/OP =(x1+x2)/(x1*OA)

And

1/OQ = (x1-x2)/(x1*OA)

Now, we add them and we get

1/OP+1/OQ= 2/OA

Which means that OA is the HM of OP and OQ