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Question Number 52533 by Tawa1 last updated on 09/Jan/19

Commented by ajfour last updated on 09/Jan/19

Commented by ajfour last updated on 10/Jan/19
$ρ = r+2R = a(√2) r+R = R(√2) ⇒ r = R((√2)−1) ρ = R((√2)−1+2)= a(√2) shaded area A= 4a^2 −πr^2 −2πR^2 −4R^2 = 2R^2 ((√2)+1)^2 −4R^2 −πR^2 [2+((√2)−1)^2 ] =R^2 {6+4(√2)−4−π(5−2(√2))} = 4{2+4(√2)−π(5−2(√2))} = 8+16(√2)−20π+8(√2)π = 8+(16+8π)(√2)−20π a+b+c+d = 8+16+8−20 = 12 .$
$ρ = r + 2 R = a \sqrt{2}$ $r + R = R \sqrt{2}$ $\Rightarrow r = R (\sqrt{2} - 1)$ $ρ = R (\sqrt{2} - 1 + 2) = a \sqrt{2}$ $s h a d e d a r e a A = 4 a^{2} - π r^{2} - 2 π R^{2} - 4 R^{2}$ $= 2 R^{2} {(\sqrt{2} + 1)}^{2} - 4 R^{2} - π R^{2} [2 + {(\sqrt{2} - 1)}^{2}]$ $= R^{2} {6 + 4 \sqrt{2} - 4 - π (5 - 2 \sqrt{2})}$ $= 4 {2 + 4 \sqrt{2} - π (5 - 2 \sqrt{2})}$ $= 8 + 16 \sqrt{2} - 20 π + 8 \sqrt{2} π$ $= 8 + (16 + 8 π) \sqrt{2} - 20 π$ $a + b + c + d = 8 + 16 + 8 - 20 = 12 .$
Commented by Tawa1 last updated on 09/Jan/19

$God bless you sir .$
Commented by Tawa1 last updated on 09/Jan/19

$Sir, they said the answer is 12 .$
Commented by Tawa1 last updated on 10/Jan/19

$Thanks for checking sir$
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