CAT Exam Model Paper 7 with solutions for free online practice

Question : 11 of 60

Marks: +1, -0

Let P be a point on the side AB of a triangle ABC. Lines drawn parallel to PC, through the points A and B, meet BC and AC extended at X and Y respectively. The lengths of AX, BY and PC are ‘a’ units, 'b’ units and ‘c’ units respectively. Then c will be equal to the half of

Arithmetic Mean of a and b
Geometric Mean of a and b
Harmonic Mean of a and b
None of these

Validate

Solution:

Let AP = x , PB = y
Now, ∆APC is similar to ∆ABY.
Therefore

{x}/{x+y}= {c}/{b}

...(i)
Similarly, ∆ABX is similar to ∆PBC.
Hence

{y}/{x+y}= {c}/{a}

...(ii)
(i) & (ii) gives

{1}/{c}= {1}/{a}+ {1}/{b}

c= {a b}/{a+b}

c= {1}/{2}(

Harmonic mean of a and b)

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