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Question Number 139053 by mathocean1 last updated on 21/Apr/21

Commented by mathocean1 last updated on 21/Apr/21

$$DeterminateR$$

Answered by mr W last updated on 21/Apr/21

$$x^2+{30}^2=R^2...\left(i\right)$$$${(x+d)}^2+{24}^2=R^2...\left(ii\right)$$$${(x+2d)}^2+{12}^2=R^2...\left(iii\right)$$$$\left(iii\right)-\left(ii\right):$$$$d(2x+3d)-12\times 36=0...\left(iv\right)$$$$\left(ii\right)-\left(i\right):$$$$d(2x+d)-6\times 54=0...\left(v\right)$$$$\left(iv\right)-\left(v\right):$$$$2d^2-12\times 36+6\times 54=0$$$$\Rightarrow d=3\sqrt{6}$$$$3\sqrt{6}(2x+3\sqrt{6})=6\times 54$$$$\Rightarrow x=\frac{15\sqrt{6}}{2}$$$${\left(\frac{15\sqrt{6}}{2}\right)}^2+{30}^2=R^2$$$$\Rightarrow R=\frac{15\sqrt{22}}{2}\approx 35.178$$

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