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A-circle-tangents-to-x-and-y-axes-and-x-1-2-y-1-2-a-1-2-find-its-radious-

Question Number 58282 by behi83417@gmail.com last updated on 20/Apr/19 $$\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{circle}}\:\boldsymbol{\mathrm{tangents}}\:\boldsymbol{\mathrm{to}}\::\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{y}}\:\boldsymbol{\mathrm{axes}}\:\boldsymbol{\mathrm{and}} \\ $$$$\:\:\:\:\boldsymbol{\mathrm{x}}^{\frac{\mathrm{1}}{\mathrm{2}}} +\boldsymbol{\mathrm{y}}^{\frac{\mathrm{1}}{\mathrm{2}}} =\boldsymbol{\mathrm{a}}^{\frac{\mathrm{1}}{\mathrm{2}}} .\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{radious}}. \\ $$ Answered by mr W last updated on 21/Apr/19…

Question-189290

Question Number 189290 by normans last updated on 14/Mar/23 Answered by a.lgnaoui last updated on 14/Mar/23 $$\:\:\bigtriangleup\boldsymbol{{ABC}}\:\:\left[\measuredangle{OAC}={x}\:\:\:\measuredangle{BAO}={y}\right] \\ $$$$\:\:\:\:\:\:\:\:{x}+{y}=\mathrm{180}−\mathrm{126}=\mathrm{54}\:\: \\ $$$$\:\:\bigtriangleup\boldsymbol{{AOB}}\::\:\:\:\:\frac{\mathrm{sin}\:\mathrm{25}}{{OA}}=\frac{\mathrm{sin}\:{y}}{{OB}}\:\:\:\:\:\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\:\:\bigtriangleup\boldsymbol{{AOC}}\::\:\:\:\frac{\mathrm{sin}\:\mathrm{17}}{{OA}}=\frac{\mathrm{sin}\:{x}}{{OC}}\:\:\:\:\:\:\:\:\:\:\left(\mathrm{2}\right) \\ $$$$\:\:\:\:\frac{\left(\mathrm{1}\right)}{\left(\mathrm{2}\right)}\Rightarrow\frac{\mathrm{sin}\:\mathrm{25}}{\mathrm{sin}\:\mathrm{17}}=\frac{\mathrm{sin}\:{y}}{\mathrm{sin}\:{x}}×\frac{{OC}}{{OB}}\:\:\:\:\:\:\:\:\left(\mathrm{3}\right)…