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Category: Geometry

Question-135712

Question Number 135712 by Dwaipayan Shikari last updated on 15/Mar/21 Commented by Dwaipayan Shikari last updated on 15/Mar/21 $${Smaller}\:{circle}\:{has}\:{half}\:{of}\:{the}\:{radius}\:{of}\:{the}\:{larger}\:{circle}. \\ $$$${Prove}\:{that},\:{irrespective}\:{of}\:{any}\:{position}\:{oc}\:{the}\:{smaller}\:{circle}\: \\ $$$${that}\:{blue}\:{point}\:{will}\:{always}\:{stay}\:{on}\:{the}\:{diametre}\:{of}\:{that}\: \\ $$$${larger}\:{circle}…

What-is-the-equation-of-ellipse-with-center-1-2-excentricity-1-3-passing-through-2-2-2-2-3-

Question Number 135695 by liberty last updated on 15/Mar/21 $${What}\:{is}\:{the}\:{equation}\:{of} \\ $$$${ellipse}\:{with}\:{center}\:\left(\mathrm{1},−\mathrm{2}\right)\: \\ $$$${excentricity}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\:,\:{passing} \\ $$$${through}\:\left(\mathrm{2},\:\frac{\mathrm{2}\sqrt{\mathrm{2}}−\mathrm{2}}{\mathrm{3}}\right)\: \\ $$ Answered by mr W last updated on…

Question-4612

Question Number 4612 by Rasheed Soomro last updated on 14/Feb/16 Commented by Rasheed Soomro last updated on 14/Feb/16 $$\:{A}\:\:{triangle}\:{divides}\:\:{its} \\ $$$${circum}-{circle}\:{in}\:{three}\:{arcs} \\ $$$${say}\:\:\boldsymbol{\mathrm{c}}_{\mathrm{1}} ,\boldsymbol{\mathrm{c}}_{\mathrm{2}} ,\boldsymbol{\mathrm{c}}_{\mathrm{3}}…

4x-2-5-2x-2-4-dx-x-0-

Question Number 4594 by alimyao last updated on 10/Feb/16 $$\int\mathrm{4}{x}^{\mathrm{2}} \:−\:\frac{\mathrm{5}}{\mathrm{2}{x}^{−\mathrm{2}} }\:+\:\mathrm{4}\:\:{dx},\:{x}\neq\mathrm{0} \\ $$$$ \\ $$ Answered by FilupSmith last updated on 10/Feb/16 $$=\mathrm{4}\int{x}^{\mathrm{2}} {dx}−\frac{\mathrm{5}}{\mathrm{2}}\int{x}^{\mathrm{2}}…

Question-70121

Question Number 70121 by ahmadshahhimat775@gmail.com last updated on 01/Oct/19 Answered by mind is power last updated on 01/Oct/19 $${let}\:{a}\:{angle}\:{left}\:−,{c}\:{side}\:{of}\:{squar} \\ $$$$\Rightarrow{c}=\mathrm{6}{sin}\left({a}\right) \\ $$$$\frac{\mathrm{6}{sin}\left({a}\right)+\mathrm{6}{cos}\left({a}\right)}{{sin}\left(\mathrm{45}\right)}=\frac{\mathrm{10}}{{sin}\left(\mathrm{45}+{a}\right)} \\ $$$$\Rightarrow\mathrm{6}.\left({sin}\left({a}\right)+{cos}\left({a}\right)\right).{sin}\left(\mathrm{45}+{a}\right)=\mathrm{10}{sin}\left(\mathrm{45}\right)…

The-segment-between-the-mid-points-of-two-sides-of-a-triangle-is-parallel-to-the-third-side-and-half-as-long-

Question Number 4578 by Rasheed Soomro last updated on 08/Feb/16 $${The}\:{segment}\:{between}\:{the}\:{mid}-{points} \\ $$$${of}\:{two}\:{sides}\:{of}\:{a}\:{triangle}\:{is}\:{parallel} \\ $$$${to}\:{the}\:{third}\:{side}\:{and}\:{half}\:{as}\:{long}.\: \\ $$ Commented by Yozzii last updated on 08/Feb/16 $${Prove}\:{this}\:{theorem}?…

In-a-right-triangle-the-mid-point-of-the-hypotenuse-is-equidistant-from-all-the-three-vertices-of-the-triangle-

Question Number 4579 by Rasheed Soomro last updated on 08/Feb/16 $${In}\:{a}\:{right}\:{triangle},\:{the}\:{mid}-{point}\:{of}\:{the} \\ $$$${hypotenuse}\:{is}\:{equidistant}\:{from}\:{all}\:{the} \\ $$$${three}\:{vertices}\:{of}\:{the}\:{triangle}. \\ $$ Commented by Yozzii last updated on 08/Feb/16 $${Prove}\:{this}\:{theorem}?…