p-is-a-point-inside-onside-outside-of-equilateral-triangle-find-side-of-triangle-if-distance-of-p-from-vertices-of-triangle-be-equail-to-5-7-11-study-each-conditions-separately-find-side-of-A

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Question Number 81267 by behi83417@gmail.com last updated on 10/Feb/20

$$\mathbf{p},\mathrm{is}\mathrm{a}\mathrm{point},\mathbf{inside},\mathbf{onside},\mathbf{outside}\mathrm{of}$$$$\mathrm{equilateral}\mathrm{triangle}.\mathrm{find}\mathrm{side}\mathrm{of}\mathrm{triangle}$$$$\mathrm{if}\mathrm{distance}\mathrm{of}:\mathbf{p}\mathrm{from}\mathrm{vertices}\mathrm{of}\mathrm{triangle}$$$$\mathrm{be}\mathrm{equail}\mathrm{to}:5,7,11.$$$$\left(\mathrm{study}\mathrm{each}\mathrm{conditions}\mathrm{separately}\right).$$$$\mathrm{find}\mathrm{side}\mathrm{of}\mathrm{ABC}\mathrm{and}{\mathrm{p}}_1{\mathrm{p}}_2{\mathrm{p}}_3\mathrm{in}\mathrm{a}$$$$\mathrm{special}\mathrm{case}\mathrm{that}:\{\begin{array}{l}{\mathrm{Ap}}_1=11\\ {\mathrm{Bp}}_2=5\\ {\mathrm{Cp}}_3=7\end{array}$$

Commented by behi83417@gmail.com last updated on 10/Feb/20

Commented by mr W last updated on 10/Feb/20

$$sir:{it}^{\prime }snotclearwhatismeant.$$$$ifthedistancefromapointP,which$$$$canlieinside,onsideoroutsideofthe$$$$triangle,tothevertexesofthetriangle$$$$is5,7,11respectively,thentheside$$$$lengthofthetriangleisalsofixed,$$$$generallytherearetwovalues.$$$$$$$$justtohave{AP}_1=11,{BP}_2=5and$$$${CP}_3=7,ABCand{P}_1{P}_2{P}_{3}couldbeof$$$$infinitelymanysizes,i.e.youcan$$$$notdeterminetrianglesABCand{P}_1{P}_2{P}_3$$$$usingonlythiscondition.$$

Commented by behi83417@gmail.com last updated on 11/Feb/20

$$\mathrm{thank}\mathrm{you}\mathrm{dear}\mathrm{master}.\mathrm{there}\mathrm{is}3\mathrm{separate}$$$$\mathrm{questions}:$$$$1.\mathrm{p},\mathrm{is}\mathrm{inside}\mathrm{of}\mathrm{triangle}\mathrm{and}\mathrm{its}\mathrm{distances}$$$$\mathrm{from}\mathrm{vertices}\mathrm{are}:5,7,11.\mathrm{and}\mathrm{so}\mathrm{on}\mathrm{for}$$$$\text{You can't use 'macro parameter character \#' in math mode}$$$$\mathrm{each}\mathrm{colore}\mathrm{is}\mathrm{for}\mathrm{one}\mathrm{question}.$$

Commented by behi83417@gmail.com last updated on 11/Feb/20

Commented by mr W last updated on 11/Feb/20

$$isee.$$$$butifthethreedistancesaregiven,$$$$wecanuniquelydeterminethe$$$$correspondingequilateraltriangle.$$$$wecanthencheckifthepointis$$$$inside,onsideoroutsidethetriangle.$$$$butthisisalreadysolvedinanearlier$$$$postofyou.$$

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