Question

In the figure, the sides $AB,BC$ and $CA$ of a triangle $ABC,$ touch a circle at $P,Q$ and $R$ respectively. If $PA=4$ cm, $BP=3$ cm and $AC=11$ cm, then the length of $BC$ (in cm) is:

• A. $11$
• B. $10$
• C. $14$
• D. $15$

Answer 1

Answer: (B)

$10$

As given

$PA=4cm$

$BP=3cm$

$\therefore AB=4+3=7cm$

$AC=11cm$

As $PA$ and $RA$ is two tangents from same external point $A$

$\therefore RA=PA=4cm$

$\Rightarrow RC=AC-RA$

$\Rightarrow RC=11-4=7cm$

As $RC$ and $QC$ is two tangents from same external point $C$

$\therefore QC=RC=7cm$

As $BP$ and $BQ$ is two tangents from same external point $B$

$\therefore BP=BQ=3cm$

Then $BC=QC+BQ$

$\Rightarrow BC=7+3=10cm$