Category: Geometry

Question Number 200325 by cherokeesay last updated on 17/Nov/23 $$\mathrm{A}\mathrm{point}\mathrm{P}\mathrm{is}\mathrm{taken}\mathrm{inside}\mathrm{the}\mathrm{rectangleC}$$$$\mathrm{ABD}.\mathrm{This}\mathrm{point}\mathrm{joins}\mathrm{the}\mathrm{four}\mathrm{vertices}\mathrm{ofh}$$$$\mathrm{te}\mathrm{rectangle}.\mathrm{Knowing}\mathrm{that}\mathrm{PA}\mathrm{is}15\mathrm{cm}.\mathrm{B}$$$$\mathrm{P}24\mathrm{cm}\mathrm{and}\mathrm{PC}20\mathrm{cm}\mathrm{find}\mathrm{the}\mathrm{distancef}$$$$\mathrm{o}\mathrm{point}\mathrm{P}\mathrm{from}\mathrm{point}\mathrm{D}.$$ Answered by som(math1967) last updated…

Question Number 200204 by cherokeesay last updated on 15/Nov/23 Commented by MM42 last updated on 15/Nov/23 $$is,ABCD,issquare?$$ Commented by ajfour last updated on…

Question Number 200092 by ajfour last updated on 13/Nov/23 Commented by ajfour last updated on 13/Nov/23 $$Ifsemicirclehasradius1,find$$$$radiiofblueandgreencircles.$$$$Oneendofeachsemicircleisat$$$$centerofother.$$…

Question Number 199911 by mr W last updated on 11/Nov/23 Commented by mr W last updated on 11/Nov/23 $$threemirrorsbuildthesidesofan$$$$equilateraltriangle.alaserray$$$$emittedfromthemidpointofaside$$$${should}\:{reach}\:{the}\:{opposite}\:{vertex}\:{after}…

Question Number 199728 by Mingma last updated on 08/Nov/23 Answered by AST last updated on 08/Nov/23 $$\frac{sin120°}{BC}=\frac{sin20°}{AB}\Rightarrow AB=\frac{2\sqrt{3}BCsin20°}{3}$$$$\frac{sin20°}{AB}=\frac{sin40°}{AC}\Rightarrow AC=2ABcos20°=\frac{2\sqrt{3}BCsin40}{3}$$$$\frac{sin\left(x\right)}{DC}=\frac{sinADC}{AC}=\frac{sin(140-x)}{AC}\Rightarrow \frac{AC}{DC}=\frac{sin(140-x)}{sin\left(x\right)}$$$$=\frac{sin40}{sin20}=2cos20=\frac{sin140cosx-sin\left(x\right)cos\left(140\right)}{sinx}$$$$={sin}\mathrm{40}{tan}\left({x}\right)−{cos}\left(\mathrm{90}+\mathrm{50}\right)={sin}\mathrm{40}{tanx}+{sin}\mathrm{50}…