Construct an isosceles triangle $A B C$ such that
$A B = 6 c m, B C = A C = 4 c m .$ Bisect $∠ C$ internally and mark a point $P$ on this bisector such that $C P = 5 c m .$ Find the points $Q$ and $R$ which are $5$ $c m$ from $P$ and also $5$ $c m$ from the line $A B$ .

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Solution

$\begin{matrix} S t e p s o f c o n s t r u c t i o n : (i) D r a w A B = 6 c m a n d c u t a r c o f 4 c m f r o m A a n d B t h e s e a r c s i n t e r s e c t a t C j o i n A C a n d B C . (i i) D r a w t h e b i s e c t o r (i n t e r n a l) o f ∠ C a n d m a r k t h e p o i n t P, t a k i n g C P = 5 c m . (i i i) D r a w a l i n e E F p a r a l l e l t o A B a t a d i s tan c e o f 5 c m . (i v) T a k e P a s c e n t r e c u t t w o p o i n t s o n l i n e E F a s P Q a n d P R a r e e a c h e q u a l t o 5 c m . \end{matrix}$

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