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Question Number 212801 by Spillover last updated on 24/Oct/24

Answered by som(math1967) last updated on 24/Oct/24

Commented by som(math1967) last updated on 24/Oct/24

$$\frac{OL}{PL}=\tan 22\frac{1}{2}$$$$PL=6(\sqrt{2}+1)$$$$PL=PM=6(\sqrt{2}+1)$$$$\frac{MN}{PM}=\tan 30$$$$MN=\frac{6(\sqrt{2}+1)}{\sqrt{3}}$$$$\therefore R=\frac{6(\sqrt{2}+1)}{\sqrt{3}}$$

Answered by mr W last updated on 24/Oct/24

$$\frac{R}{\tan \frac{60°}{2}}=\frac{6}{\tan \frac{45°}{2}}$$$$\Rightarrow R=\frac{2\sqrt{3}}{\sqrt{2}-1}=2\sqrt{3}(\sqrt{2}+1)$$

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