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Question

ABC is a right angled triangle, right angled at B. BD is perpendicular as shown. If AD: DC = 1:2, then AB2BC2 is:


  1. 1: 2

  2. 1: 4

  3. 4: 1

  4. 2: 1


Solution

The correct option is A

1: 2


Consider  ADB and  ABC
∠BAD =  ∠BAC    [common angle]
∠BDA =  ∠ABC     [ 90]
Therefore by AA similarity criterion, ADB and  ABC are similar.
So,  ABACADAB
 AB2 = AC . AD  -------------(I)

Similarly,  BDC and ABC are similar.
So,  BCACDCBC
 BC2 = AC . DC  -------------(II)
Dividing (I) and (II) and cancelling out AC, we get, (ABBC)2ADDC -------------(III)
So, the ratio is the same, i.e., 1: 2.

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