In rectangle ABCD, AB =8 and BC = 20. Let P be a point on AD such that angle BPC=90° . If r1 ,r2, r3 are the radii of the incircles of triangles APB, BPC and COD, what is the value of r1+r2+r3 ?

Asked by vikasg13.hardware | 13th Jun, 2018, 12:07: PM

Expert Answer:

Let BP = x then PC = 20 - x
In ΔABP
BP2 = 82 + x2 and PD2 = 82 + (20 - x)2 
In ΔAPD
82 + x2 + 82 + (20 - x)2 = 202 
we get x = 4, 16
begin mathsize 16px style Radius space of space inscribed space circle space equals space fraction numerator 2 straight A over denominator open parentheses straight a plus straight b plus straight c close parentheses end fraction
end style
Find r1, r2, r3 and then r1 +  r2 + r3

Answered by Sneha shidid | 14th Jun, 2018, 10:55: AM

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