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Question Number 168324 by leicianocosta last updated on 07/Apr/22

Answered by mr W last updated on 08/Apr/22

Commented by mr W last updated on 08/Apr/22

$$c=x\cos \theta$$$$a=12-x\cos \theta$$$$b=18-x\cos \theta$$$$R=x\sin \theta$$$$2({\tan }^{-1}\frac{12-x\cos \theta }{x\sin \theta }+{\tan }^{-1}\frac{18-x\cos \theta }{x\sin \theta })=\pi -\mathrm{\angle }C=2\theta$$$${\tan }^{-1}\frac{12-x\cos \theta }{x\sin \theta }+{\tan }^{-1}\frac{18-x\cos \theta }{x\sin \theta }=\theta$$$$\frac{\frac{12-x\cos \theta }{x\sin \theta }+\frac{18-x\cos \theta }{x\sin \theta }}{1-\frac{12-x\cos \theta }{x\sin \theta }\times \frac{18-x\cos \theta }{x\sin \theta }}=\tan \theta$$$$x^2=12\times 18$$$$\Rightarrow x=6\sqrt{6}$$

Commented by Tawa11 last updated on 08/Apr/22

$$\mathrm{Great}\mathrm{sir}$$

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