Question Number 224615 by necx122 last updated on 21/Sep/25 $${The}\:{vectors}\:{OP},\:{OQ}\:{and}\:{OR}\:{represented} \\ $$$${by}\:{a},{b}\:{and}\:{c}\:{respectively}:\:{where}\:{a}=\mathrm{10}{i}+{j}, \\ $$$${b}=−\mathrm{2}{i}+\mathrm{7}{j},\:{c}={a}+\mathrm{3}{b},\:{and}\:{O}\:{is}\:{the}\:{origin}. \\ $$$${OR}\:{and}\:{PR}\:{intersects}\:{at}\:{M}\:{where} \\ $$$${OM}={kOR}\:{and}\:{PM}={lPQ}\:{and}\:{k},\:{l}\:{are} \\ $$$${constants}.\:{Find}: \\ $$$$\left({i}\right)\:{The}\:{equation}\:{of}\:{the}\:{lines}\:{of}\:{PQ}\:{and} \\ $$$${OR} \\…
Question Number 224608 by fantastic last updated on 21/Sep/25 Commented by fantastic last updated on 21/Sep/25 $$\measuredangle{EFD}=? \\ $$ Answered by som(math1967) last updated on…
Question Number 224591 by Jyrgen last updated on 22/Sep/25 $$\mathrm{p}\:{is}\:{a}\:{prime}\:{number} \\ $$$${prove}\:{that}\:{if}\:\mathrm{p}^{\mathrm{2}} +\mathrm{8}\:{is}\:{prime}\:\Rightarrow \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:{p}^{\mathrm{3}} +\mathrm{4}\:{is}\:{also}\:{prime} \\ $$ Answered by Ghisom_ last updated on 22/Sep/25…
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Question Number 224592 by Nicholas666 last updated on 20/Sep/25 Commented by Nicholas666 last updated on 20/Sep/25 $$\:\:\:\:\:\mathrm{The}\:\mathrm{medians}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:{ABC}\:\:\mathrm{cut}\:\mathrm{it}\:\mathrm{into}\:\mathrm{6}\:\mathrm{triangles}.\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{centers}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circum}\:\mathrm{scribed}\:\mathrm{circles}\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{of}\:\mathrm{these}\:\mathrm{triangles}\:\mathrm{lie}\:\mathrm{ln}\:\mathrm{the}\:\mathrm{same}\:\mathrm{circle}.\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{How}\:\mathrm{is}\:\mathrm{this}\:\mathrm{theorem}\:\mathrm{called}? \\ $$$$…
Question Number 224594 by Nicholas666 last updated on 20/Sep/25 $$ \\ $$$$\:\:\:\:\mathrm{let}\:{I}\:\mathrm{be}\:\mathrm{the}\:\mathrm{incenter}\:\mathrm{of}\:\mathrm{a}\:\mathrm{non}−\mathrm{isosceles}\:\:\Delta{ABC}\:\:\:\:\:\: \\ $$$$\:\:\:\:\mathrm{and}\:\mathrm{let}\:\mathrm{the}\:\mathrm{incircle}\:\mathrm{be}\:\mathrm{tanget}\:\mathrm{to}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{point}\:{D},{E},{F}.\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\mathrm{the}\:\mathrm{line}\:{AI}\:\mathrm{intersects}\: \left({ABC}\right)\:\mathrm{at}\:{A}\:\mathrm{and}\:{S}. \\ $$$$\:\:\:\:\:\mathrm{the}\:\mathrm{line}\:{SD}\:\mathrm{intersects}\: \left({ABC}\right)\:\mathrm{at}\:{S}\:\mathrm{and}\:{T}.\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{let}\:{IT}\:\cap\:{EF}\:={M},\: \left({BIC}\right)\:\cap\: \left({DEF}\right)={K},{L}. \\…
Question Number 224558 by ajfour last updated on 19/Sep/25 Commented by ajfour last updated on 19/Sep/25 Commented by ajfour last updated on 19/Sep/25 Commented by…
Question Number 224568 by fkwow344 last updated on 19/Sep/25 $$\sqrt{{x}}={a\begin{cases}{{a}\in\mathbb{Z}=\mathrm{0}}\\{{a}\notin\mathbb{Z}=\mathrm{1}}\end{cases}} \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{3}} \:\sqrt{{x}}{dx}=? \\ $$ Commented by Ghisom_ last updated on 19/Sep/25 $$\mathrm{what}\:\mathrm{does}\:\mathrm{this}\:\mathrm{mean}? \\…