Three circles centered at points A,B,C and of radii 5,5 and 8 units resp., touch each other externally. Two circles C1 and C2 one smaller and other bigger , touch all three circles. Then the radius of
 
a) c1 is 8/9 units                                                    b) c2 is 40/3 units
 
c) incircle of Triangle ABC is 10/3 units                     d) incircle of triangle ABC is 28/9 units
 

Asked by Sunil Soni | 10th Aug, 2016, 05:25: PM

Expert Answer:

 
 
 
 
 
 
In space increment ABC space draw space straight a space perpendicular space from space straight c space on space side space AB space touching space at space straight P.
As space space increment ABC space is space an space isoscales space triangle comma
therefore CP space divides space AB space in space two space parts.
rightwards double arrow AP space equals PB space equals space 5 units.

In space increment APC comma space using space Pythagoras space theorem space we space get comma
AC squared space equals space PC squared plus AP squared
13 squared equals space PC squared plus 5 squared
PC space equals space 12 space units.

radius space of space incircle space of space straight a space tirangle
equals fraction numerator Area space of space the space triangle over denominator semiperimetre space of space the space triangle end fraction

Radius space of space incircle space of space straight a space tirangle space ABC
equals fraction numerator begin display style 1 half cross times 10 cross times 12 end style over denominator 1 half cross times open parentheses 10 plus 13 plus 13 close parentheses end fraction equals 120 over 36 equals 10 over 3 units

Option space left parenthesis straight C right parenthesis space space is space correct.

Answered by Vijaykumar Wani | 11th Aug, 2016, 01:00: PM

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