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Question Number 86937 by TawaTawa1 last updated on 01/Apr/20

Commented by john santu last updated on 01/Apr/20

radius smaller circle = (8/(15)) miss tawa

$$\mathrm{radius}\:\mathrm{smaller}\:\mathrm{circle}\:=\:\frac{\mathrm{8}}{\mathrm{15}} \\ $$$$\mathrm{miss}\:\mathrm{tawa} \\ $$

Commented by john santu last updated on 01/Apr/20

Commented by john santu last updated on 01/Apr/20

cos θ = cos θ ((2R)/(3x(√5))) = (x/(4(√5))) ⇒ R = ((3x^2 )/8) ...(i) 12^2 = (4(√5))^2 + (3x(√5) )^2 144−80 = 45x^2 ⇒ x^2 = ((64)/(45)) ...(ii) ⇒ R = (3/8)×((64)/(45)) = (8/(15))

$$\mathrm{cos}\:\theta\:=\:\mathrm{cos}\:\theta \\ $$$$\frac{\mathrm{2R}}{\mathrm{3x}\sqrt{\mathrm{5}}}\:=\:\frac{\mathrm{x}}{\mathrm{4}\sqrt{\mathrm{5}}}\:\Rightarrow\:\mathrm{R}\:=\:\frac{\mathrm{3x}^{\mathrm{2}} }{\mathrm{8}}\:...\left(\mathrm{i}\right) \\ $$$$\mathrm{12}^{\mathrm{2}} \:=\:\left(\mathrm{4}\sqrt{\mathrm{5}}\right)^{\mathrm{2}} \:+\:\left(\mathrm{3x}\sqrt{\mathrm{5}}\:\right)^{\mathrm{2}} \\ $$$$\mathrm{144}−\mathrm{80}\:=\:\mathrm{45x}^{\mathrm{2}} \:\Rightarrow\:\mathrm{x}^{\mathrm{2}} \:=\:\frac{\mathrm{64}}{\mathrm{45}}\:...\left(\mathrm{ii}\right) \\ $$$$\Rightarrow\:\mathrm{R}\:=\:\frac{\mathrm{3}}{\mathrm{8}}×\frac{\mathrm{64}}{\mathrm{45}}\:=\:\frac{\mathrm{8}}{\mathrm{15}} \\ $$

Commented by TawaTawa1 last updated on 01/Apr/20

God bless you sir, i appreciate your time

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir},\:\:\mathrm{i}\:\mathrm{appreciate}\:\mathrm{your}\:\mathrm{time} \\ $$

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