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F i n d space t h e space e q u a t i o n space o f space t h e space c i r c l e space w h o s e space c e n t r e space i s space t h e space c e n t r o i d space o f space t h e space t r i a n g l e space w i t h space v e r t i c e s
A left parenthesis 1 comma 2 right parenthesis space comma space B left parenthesis 2 comma 3 right parenthesis space comma space C left parenthesis 3 comma 1 right parenthesis space a n d space t o u c h e s space t h e space s i d e space A B.

Please provide solution to this question

Asked by Topperlearning User 15th November 2016, 10:26 PM
Answered by Expert
Answer:

L e t space t h e space v e r t i c e s space b e space
A equals left parenthesis 1 comma 2 right parenthesis
B equals left parenthesis 2 comma 3 right parenthesis
C equals left parenthesis 3 comma 1 right parenthesis
C e n t r o i d space i s space G equals open parentheses fraction numerator 1 plus 2 plus 3 over denominator 3 end fraction comma fraction numerator 2 plus 3 plus 1 over denominator 3 end fraction close parentheses equals open parentheses 2 comma 2 close parentheses
G i v e n space t h i s space c i r c l e space t o u c h e s space space t h e space s i d e space A B space o f space t h e space t r i a n g l e
R a d i u s space w i l l space b e space t h e space p e r p e n d i c u l a r space d i s tan c e space o f space t h e space c e n t r o i d space f r o m space t h e space s i d e space A B

E q u a t i o n space o f space A B space i s space g i v e n space b y
fraction numerator y minus 2 over denominator 3 minus 2 end fraction equals fraction numerator x minus 1 over denominator 2 minus 1 end fraction
rightwards double arrow x minus y plus 1 equals 0
R a d i u s equals open vertical bar fraction numerator 2 minus 2 plus 1 over denominator square root of 1 plus 1 end root end fraction close vertical bar equals fraction numerator 1 over denominator square root of 2 end fraction
R e q u i r e d space e q u a t i o n space i s
left parenthesis x minus 2 right parenthesis squared plus left parenthesis y minus 2 right parenthesis squared equals 1 half
rightwards double arrow 2 x squared plus 2 y squared minus 8 x minus 8 y plus 15 equals 0

Answered by Expert 16th November 2016, 12:26 AM
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