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Q.

In the given figure, QA and PB are perpendiculars to AB. If AO=10cm , BO=6cm and PB=9cm, then AQ is,


1008667

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a

10 cm

b

15 cm

c

20 cm

d

24 cm 

answer is B.

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Detailed Solution

Given figure is,
1008667Also given, AO=10cm , BO=6cm and PB=9cm.
According to the question, as PB and AQ are perpendicular to AB, the angles ∠AOQ   and ∠BOP   are vertically opposite angles. So they are equal.
⇒ ∠AOQ=∠BOP  .
As the angles, ∠OAQ   and ∠OBP   are right angles. So they are equal.
⇒ ∠OAQ=∠OBP  .
So, by the AA similarity criterion.
The triangles ΔOAQ and ΔOBP are similar.
⇒ ΔOAQ~ΔOBP  
As the triangles are similar,
Then sides ratio of triangles ΔOAQ and ΔOBP are equal.
Therefore,
AO BO = AQ PB  .
⇒ 10 6 = AQ 9 ⇒AQ= 5 9 3 ⇒AQ=15 cm  
The value of the AQ is 15cm.
Hence, option 2 is correct.
 
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