SATHEE: Quantitative Aptitude Ques 2119

Quantitative Aptitude Ques 2119

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=6cm, $ then perimeter of $ \Delta ABC $ is

Options:

A) $ 6cm $

B) $ 10cm $

C) $ 12cm $

D) $ 18cm $

Show Answer

Answer:

Correct Answer: C

Solution:

We know that, the length of tangents drawn to a circle from any external point are equal.

$ \therefore $ $ AQ=AR $ (i) $ BP=BQ $ (ii) and $ CP=CR $ … (iii) Now. perimeter of $ \Delta ABC=AB+BC+AC $ $ =AB+BP+CP+AC $ Here, $ BQ=BP $ and $ CP=CR $ $ =AB+BQ+CR+AC $ [using Eqs. (ii) and (iii)] $ AB+BQ=AQ $ … (iv) $ AC+CR=AR $ … (v) Now, adding Eqs. (iv) and (v) $ AB+BQ+AC+CR=AQ+AR $ [Now, AQ = AR]

$ \Rightarrow $ $ AB+BQ+AC+CR=2AQ $ $ =2\times 6=12 $ Now, perimeter of $ \Delta ABC=2\times 6=12 $

Quantitative Aptitude Ques 2118

Quantitative Aptitude Ques 2120

Quantitative Aptitude Ques 2119

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=6cm, $ then perimeter of $ \Delta ABC $ is

Options:

Answer:

Solution:

Bank Preparation

Bank Courses

NCERT Books

Important Resources

Forum