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Question Number 166319 by cortano1 last updated on 18/Feb/22

Commented by otchereabdullai@gmail.com last updated on 18/Feb/22

$$\mathrm{nice}\mathrm{question}$$

Commented by MJS_new last updated on 18/Feb/22

$$\mathrm{for}\mathrm{any}\mathrm{given}\mathrm{triangle}\mathrm{with}\mathrm{sides}a,b,c\mathrm{and}$$$$a\mathrm{being}\mathrm{the}\mathrm{base}\mathrm{line}(\mathrm{orientation}\mathrm{as}\mathrm{in}\mathrm{the}$$$$\mathrm{given}\mathrm{picture}):$$$$\mid DE\mid =\frac{\delta a}{\delta +a^2}\mathrm{with}\delta =\sqrt{(a+b+c)(b+c-a)(a+c-b)(a+b-c)}$$

Answered by mr W last updated on 18/Feb/22

$$5h=3\times 4\Rightarrow h=2.4$$$$\frac{2r}{5}=\frac{2.4-r}{2.4}$$$$r=\frac{60}{49}$$$$DE=2r=\frac{120}{49}\approx 2.449$$

Commented by Tawa11 last updated on 18/Feb/22

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

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