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Touching Circles Theorem

Two tiangles ...

Question

Two tiangles $A B C a n d P Q R$ are similar, if $B C : C A : A B = 1 : 2 : 3$ , then $\frac{Q R}{P R}$ is

A

\frac{2}{3}

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B

\frac{1}{2}

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C

\frac{1}{\sqrt{2}}

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D

\frac{1}{3}

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Solution

The correct option is B $\frac{1}{2}$
$S i n c e △ A B C a n d △ P Q R a r e s i m i l a r t h e i r s i d e s w i l l b e i n s a m e r a t i o \frac{A B}{P Q} = \frac{A C}{P R} = \frac{B C}{Q R} B C : C A : A B = 1 : 2 : 3 \Rightarrow \frac{2}{P R} = \frac{1}{Q R} \Rightarrow \frac{Q R}{P R} = \frac{1}{2} H e n c e o p t i o n (C) i s c o r r e c t a n s w e r$

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