question_answer

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

A) 6 cm                            

B) 10 cm

C) 12 cm

D) 18 cm

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)]

\[=AQ+AR\]

\[=2\,\,AQ\]       [using Eq. (i)]

\[=2\times 6=12\,cm\]