Question
Fri March 13, 2015 By: Chandana Kiran

if a b and c are the sides of a right angled triangled where c is hypotenuse the prove that the radius r of the circle which touches the sides of the triangle is given by r=a+b-c/ 2

Expert Reply
Vimala Ramamurthy
Sat March 14, 2015
C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
L e t space r space b e space t h e space r a d i u s space o f space t h e space i n s c r i b e d space c i r c l e. W e space s h a l l space u s e space t h e space f a c t space t h a t space t h e space ln e g t h space o f space t h e space tan g e n t s space f r o m space a n space e x t e r n a l space p o i n t space t o space a space c i r c l e space a r e space e q u a l. T h u s comma space Q S equals Q U equals r A n d S R equals a minus r equals R T P T equals c minus open parentheses a minus r right parenthesis close parentheses a n d P U equals b minus r S i n c e space P T equals P U comma space w e space h a v e c minus open parentheses a minus r right parenthesis close parentheses equals b minus r rightwards double arrow c minus a plus r equals b minus r rightwards double arrow 2 r equals a plus b minus c rightwards double arrow r equals fraction numerator a plus b minus c over denominator 2 end fraction
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