Quantitative Aptitude Ques 333

Question: A circle is touching the side BC of $ \Delta ABC $ at P and is also touching AB and AC produced at Q and R, respectively. If AQ = 6 cm, then perimeter of $ \Delta ABC $ is

Options:

A) 6 cm

B) 10 cm

C) 12 cm

D) 18 cm

Show Answer

Answer:

Correct Answer: C

Solution:

  • We know that, the length of tangents drawn to a circle from any external point is same. $ AQ=AR $ … (i) $ BP=BQ $ … (ii) and $ CP=CR $ … (iii) Now, perimeter of $ \Delta ABC $ $ =AB+BC+AC $ $ =AB+BP+CP+AC $ $ =AB+BQ+CR+AC $
    [using Eqs.(ii) and (iii)] $ =AQ+AR $ $ =2AQ $ [using Eq. (i)] $ =2\times 6=12,cm $
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