Category: Geometry

Question Number 80222 by mr W last updated on 01/Feb/20 Commented by mr W last updated on 01/Feb/20 $$AroundsteelplatewithradiusRhas$$$$aroundholewithradiusrasshown.$$$$Wasisthemaximalareaoftheellipse$$$${which}\:{can}\:{be}\:{cut}\:{off}\:{from}\:{the}\:{plate}?…

Question Number 14630 by Don sai last updated on 03/Jun/17 $$\mathrm{solve}\mathrm{the}\mathrm{eqn}$$$$\mathrm{dr}/\mathrm{d}\theta =[\mathrm{r}({\mathrm{a}}^2-{\mathrm{r}}^2)/{\mathrm{a}}^2+{\mathrm{r}}^2]\cot \theta$$$$\mathrm{hint}.\:\mathrm{let}\:\mathrm{a}^{\mathrm{2}} +\mathrm{r}^{\mathrm{2}} =\mathrm{a}^{\mathrm{2}} −\mathrm{r}^{\mathrm{2}} +\mathrm{2r}^{\mathrm{2}} . \…

Question Number 145573 by mnjuly1970 last updated on 06/Jul/21 Answered by Olaf_Thorendsen last updated on 06/Jul/21 $$p=halfperimeter$$$$p=\frac{1}{2}(1+2r+2+2r+3+2r)=3(r+1)$$$$p-a=3(r+1)-(1+2r)=r+2$$$$p-b=3(r+1)-(2+2r)=r+1$$$${p}−{c}\:=\:\mathrm{3}\left({r}+\mathrm{1}\right)−\left(\mathrm{3}+\mathrm{2}{r}\right)\:=\:{r}…

Question Number 80015 by mr W last updated on 30/Jan/20 Commented by mr W last updated on 30/Jan/20 $$1.Provethatbothequilaterialtriangles$$$$toucheachotherinthesquareasshown.$$$$\mathrm{2}.\:{Find}\:{r}_{\mathrm{1}} /{r}_{\mathrm{2}} \…

Question Number 14364 by RasheedSindhi last updated on 31/May/17 $$\text{You can't use 'macro parameter character \#' in math mode}$$$${\mathrm{x}}^2+{\mathrm{y}}^2-\mathrm{xy}={\mathrm{a}}^2$$$${\mathrm{y}}^2+{\mathrm{z}}^2-\mathrm{yz}={\mathrm{b}}^2$$$${\mathrm{z}}^2+{\mathrm{x}}^2-\mathrm{zx}={\mathrm{c}}^2$$$$\mathrm{Pl}\:\mathrm{discuss}\:\mathrm{also}\:\mathrm{geometrical}/ \…