Category: Geometry

Question Number 53168 by ajfour last updated on 18/Jan/19 Commented by ajfour last updated on 19/Jan/19 $$Equilateral△ABCcontains$$$$twocirclesofradiiaandbinthe$$$$mannershown.Findtheradius$$$$Rofacirclethattouchesthesetwo$$$${circles}\:{externally}\:{and}\:{passes}\:{through}…

Question Number 53071 by behi83417@gmail.com last updated on 16/Jan/19 Commented by behi83417@gmail.com last updated on 16/Jan/19 $$asshowninfig:$$$$provethat:$$$$\to \frac{\mathbf{area}\mathbf{of}outer\mathbf{hexagon}}{\mathbf{area}\mathbf{of}inner\mathbf{triangle}}⩾13$$ Commented by…

Question Number 184135 by ajfour last updated on 03/Jan/23 Commented by mr W last updated on 03/Jan/23 $${PQ}_{min}=b\sqrt{\frac{1}{2}(1+\frac{a}{\sqrt{a^2+b^2}})}$$ Answered by…

Question Number 53031 by behi83417@gmail.com last updated on 16/Jan/19 Commented by behi83417@gmail.com last updated on 16/Jan/19 $$AB<CB.$$$$\measuredangle ABE=\measuredangle EBF=\measuredangle FBC$$$$\dots \dots showthat:\frac{\mathbf{BE}}{\mathbf{BF}}>1.$$ Answered by…

Question Number 184041 by Acem last updated on 02/Jan/23 Answered by HeferH last updated on 02/Jan/23 $$\stackrel{⌢}{TN}=\frac{\pi }{3}=\frac{180°}{3}=60°\Rightarrow \mathrm{\angle }TAN=\frac{\stackrel{⌢}{TN}}{2}=30°$$$$\mathrm{\angle }AOT=120°(△AOTisosceles)$$$$\:\angle{ATC}\:=\:\frac{\overset{\frown} {{AT}}}{\mathrm{2}}\:=\:\mathrm{60}\:\:\Rightarrow\:\angle{ACT}\:=\:\mathrm{90}°\: \…