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Category: Geometry

Question-70592

Question Number 70592 by behi83417@gmail.com last updated on 05/Oct/19 Commented by behi83417@gmail.com last updated on 05/Oct/19 $$\mathrm{convex}\:\mathrm{ABCD},\mathrm{is}\:\mathrm{given}\:\mathrm{with}: \\ $$$$\mathrm{S}\left(\mathrm{DCE}\right)=\mathrm{9},\mathrm{S}\left(\mathrm{CBE}\right)=\mathrm{10},\mathrm{S}\left(\mathrm{BAE}\right)=\mathrm{13}\:. \\ $$$$\:\:\Rightarrow\:\mathrm{S}\left(\mathrm{ADE}\right)=? \\ $$ Answered by…

Question-70590

Question Number 70590 by behi83417@gmail.com last updated on 05/Oct/19 Commented by behi83417@gmail.com last updated on 05/Oct/19 $$\mathrm{convex}\:\mathrm{ABCD},\mathrm{is}\:\mathrm{given}\:\mathrm{with}: \\ $$$$\boldsymbol{\mathrm{S}}_{\mathrm{ABCD}} =\boldsymbol{\mathrm{p}}\:\:\:,\:\:\:\:\:\mathrm{AB}+\mathrm{BD}+\mathrm{DC}=\boldsymbol{\mathrm{q}}\:\:\:. \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{maximum}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{for}}:\:\boldsymbol{\mathrm{AC}},\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{terms}} \\ $$$$\boldsymbol{\mathrm{of}}:\:\:\boldsymbol{\mathrm{p}}\:\:\boldsymbol{\mathrm{and}}\:\:\boldsymbol{\mathrm{q}}. \\…

Question-70587

Question Number 70587 by behi83417@gmail.com last updated on 05/Oct/19 Commented by behi83417@gmail.com last updated on 05/Oct/19 $$\mathrm{ABCD},\mathrm{is}\:\mathrm{given}. \\ $$$$\mathrm{AB}=\boldsymbol{\mathrm{a}},\mathrm{BC}=\boldsymbol{\mathrm{b}},\mathrm{CD}=\boldsymbol{\mathrm{c}},\mathrm{DA}=\boldsymbol{\mathrm{d}},\mathrm{AC}=\boldsymbol{\mathrm{m}},\mathrm{BD}=\boldsymbol{\mathrm{n}}. \\ $$$$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}: \\ $$$$\:\:\:\:\:\left(\boldsymbol{\mathrm{mn}}\right)^{\mathrm{2}} =\left(\boldsymbol{\mathrm{ac}}\right)^{\mathrm{2}} +\left(\boldsymbol{\mathrm{bd}}\right)^{\mathrm{2}}…

Question-70519

Question Number 70519 by TawaTawa last updated on 05/Oct/19 Commented by mr W last updated on 05/Oct/19 $${B}+{D}=\mathrm{180}° \\ $$$$\frac{{B}}{{D}}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$${B}+\frac{\mathrm{3}}{\mathrm{2}}{B}=\mathrm{180} \\ $$$$\frac{\mathrm{5}}{\mathrm{2}}{B}=\mathrm{180} \\…