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