Category: Geometry

Question Number 184398 by HeferH last updated on 06/Jan/23 Answered by som(math1967) last updated on 06/Jan/23 $$\frac{BD}{BC}=\frac{sin2\varphi }{sin(180-3\varphi )}=\frac{sin2\varphi }{sin3\varphi }$$$$\frac{AD}{BD}=\frac{sin90}{sin(90-3\varphi )}=\frac{1}{cos3\varphi }$$$$BD=ADcos3\varphi$$$$\frac{ADcos3\varphi }{AD}=\frac{sin2\varphi }{sin3\varphi }[\because BC=AD]$$$${sin}\mathrm{3}\phi{cos}\mathrm{3}\phi={sin}\mathrm{2}\phi…

Question Number 184352 by cherokeesay last updated on 05/Jan/23 Answered by som(math1967) last updated on 05/Jan/23 $$△ABC\sim △ACD$$$$\Rightarrow x^2=6\times 4\Rightarrow x=\sqrt{24}=2\sqrt{6}$$$$BC=\sqrt{4\times 2}=2\sqrt{2}$$$$\bigtriangleup{AFE}\sim\bigtriangleup{ABC} \…

Question Number 118811 by ajfour last updated on 19/Oct/20 Commented by ajfour last updated on 19/Oct/20 $$Whatisthesidelengthoftheequal$$$$sidedhexagoninscribedwithinthe$$$$triangleABCasshown?$$ Commented by…

Question Number 53252 by ajfour last updated on 19/Jan/19 Commented by ajfour last updated on 19/Jan/19 $$Findaandrintermsofb.$$ Answered by tanmay.chaudhury50@gmail.com last updated on…

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}…