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Category: Geometry

Question-184955

Question Number 184955 by mnjuly1970 last updated on 14/Jan/23 Answered by HeferH last updated on 14/Jan/23 Commented by HeferH last updated on 14/Jan/23 $$\:{A}_{{OAB}} \:=\:\frac{{a}\centerdot\mathrm{6}}{\mathrm{2}}\:=\:\frac{\pi}{\mathrm{6}}\:\centerdot\:\mathrm{6}\:\centerdot\:\frac{\mathrm{6}}{\mathrm{2}}\:=\:\mathrm{3}\pi\:\:\:\:\:\ast\left({a}\:=\:{arc}\right)\:…

Question-53792

Question Number 53792 by behi83417@gmail.com last updated on 25/Jan/19 Commented by behi83417@gmail.com last updated on 25/Jan/19 $${A}\overset{\blacktriangle} {{B}C},{equilateral}\:{with}:{AB}=\mathrm{1}. \\ $$$${circle}\:{with}\:{radius}:\:\boldsymbol{{r}}=\frac{\mathrm{1}}{\mathrm{2}\pi},\:{tangents}\:{to} \\ $$$${AC}\:{and}\:{AB}\:{at}:\:{D},{E}. \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{min}}\:\boldsymbol{\mathrm{distance}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{circle}}\:\boldsymbol{\mathrm{from}}\:\boldsymbol{\mathrm{vertices}} \\…

Question-53664

Question Number 53664 by ajfour last updated on 24/Jan/19 Commented by ajfour last updated on 24/Jan/19 $${The}\:{bases}\:{of}\:{the}\:{cones}\:{touch}\:{each} \\ $$$${other}\:{pairwise}.\:{Find}\:{the}\:{radius}\:{of} \\ $$$${the}\:{sphere}\:{tangent}\:{to}\:{all}\:{the}\:{three} \\ $$$${cones}\:{and}\:{to}\:{the}\:{plane}\:{passing} \\ $$$${through}\:{their}\:{vertices}.\:\left({semi}-{vertical}\right.…

Question-184718

Question Number 184718 by sonukgindia last updated on 10/Jan/23 Answered by HeferH last updated on 10/Jan/23 $${Let}\:\mathrm{2}{a}\:{be}\:{the}\:{side}\:{of}\:{those}\:{squares}\:{and}\:{x}\:{the}\: \\ $$$${larger}\:{side}\:{of}\:{the}\:{yellow}\:{triangle}.\: \\ $$$$\:{A}_{{rect}} =\:\mathrm{2}{a}\:\centerdot\:\mathrm{4}{a}\:=\mathrm{8}{a}^{\mathrm{2}} \\ $$$$\:{by}\:{product}\:{of}\:{chords}: \\…