Question Number 198643 by cortano12 last updated on 22/Oct/23 $$ \\ $$$$\mathrm{Given}\:\mathrm{an}\:\mathrm{isosceles}\:\mathrm{triangle}\:\mathrm{ABC} \\ $$$$\:\mathrm{which}\:\:\angle\mathrm{A}=\:\mathrm{30}°,\:\mathrm{AB}\:=\:\mathrm{AC}.\: \\ $$$$\mathrm{A}\:\mathrm{point}\:\mathrm{D}\:\mathrm{is}\:\mathrm{midpoint}\:\mathrm{of}\:\mathrm{BC}\:.\: \\ $$$$\mathrm{A}\:\mathrm{point}\:\mathrm{P}\:\mathrm{is}\:\mathrm{chosen}\:\mathrm{on}\:\mathrm{then} \\ $$$$\mathrm{segment}\:\mathrm{AD}\:\mathrm{and}\:\mathrm{a}\:\mathrm{point}\:\mathrm{Q}\:\mathrm{is} \\ $$$$\mathrm{chosen}\:\mathrm{on}\:\mathrm{the}\:\mathrm{side}\:\mathrm{AB}\:\mathrm{so}\:\mathrm{that} \\ $$$$\mathrm{BP}=\:\mathrm{PQ}. \\…
Question Number 198604 by ajfour last updated on 22/Oct/23 Commented by ajfour last updated on 22/Oct/23 $$\theta+\phi=\alpha\:\left({known}\right) \\ $$$${radius}\:{of}\:{arc}\:{is}\:{unity}. \\ $$$${If}\:{the}\:{two}\:{shaded}\:{parts}\:{are}\:{equal}, \\ $$$${find}\:\theta={f}\left(\alpha\right). \\ $$…
Question Number 198479 by ajfour last updated on 20/Oct/23 Commented by ajfour last updated on 20/Oct/23 $${Find}\:{r}\:{if}\:\alpha\:{be}\:{known}.\:{Outer}\:{circle} \\ $$$${has}\:{unit}\:{radius}. \\ $$ Commented by dangduomg last…
Question Number 198421 by mr W last updated on 19/Oct/23 Commented by mr W last updated on 19/Oct/23 $${given}\:{that}\:{the}\:{midpoints}\:{of}\:{the}\:{sides} \\ $$$${of}\:{a}\:{convex}\:{quadrilaterial}\:{are} \\ $$$${concyclic}.\:{if}\:{the}\:{lengthes}\:{of}\:{three}\:{of} \\ $$$${its}\:{sides}\:{are}\:{a},\:{b},\:{c}\:{respectively},\:{find}…
Question Number 198391 by mr W last updated on 19/Oct/23 Commented by mr W last updated on 19/Oct/23 $${prove}\:{that}\:{BE}\:{is}\:{bisector}\:{of}\:\angle{CBD}. \\ $$$$\left({B},\:{E}\:{are}\:{touching}\:{points}\right) \\ $$ Answered by…
Question Number 198235 by MASANJAJJ last updated on 15/Oct/23 Answered by Rasheed.Sindhi last updated on 15/Oct/23 $${y}={m}\angle{B}\:\:\:\:\:\:\:\left[{Corresponding}\:{angles}\right] \\ $$$${x}={m}\angle{A}\:\:\:\:\:\:\left[{Alternative}\:{angles}\right] \\ $$$${z}={m}\angle{ACB}\:\:\:\left[{Same}\:{angles}\right] \\ $$$${x}+{y}+{z}={m}\angle{A}+{m}\angle{B}+{m}\angle{ACB}=\mathrm{180}°\:\left[{Angles}\:{of}\:{triangle}\right] \\ $$$$…
Question Number 198158 by mnjuly1970 last updated on 12/Oct/23 Answered by mr W last updated on 12/Oct/23 Commented by mr W last updated on 12/Oct/23…
Question Number 198054 by necx122 last updated on 09/Oct/23 $${In}\:\bigtriangleup{MNO},\:{MN}=\mathrm{6}{units},\:{MO}=\mathrm{4}\:{units} \\ $$$${and}\:{NO}=\mathrm{12}\:{units}.\:{If}\:{the}\:{bisector}\:{of}\:{the} \\ $$$${angle}\:{M}\:{meets}\:{NO}\:{at}\:{P},\:{calculate}\:{NP}. \\ $$ Commented by som(math1967) last updated on 09/Oct/23 $${But}\:{MN}+{MO}=\mathrm{10} \\…
Question Number 198025 by mr W last updated on 08/Oct/23 Commented by mr W last updated on 08/Oct/23 $${prove}\:{PQ}={RS} \\ $$ Answered by mahdipoor last…
Question Number 197989 by mr W last updated on 07/Oct/23 Commented by mr W last updated on 07/Oct/23 $$\left[\underline{{old}\:{question}\:{from}\:{ajfour}\:{sir}}\right] \\ $$$$\mathrm{3}\:{circles}\:{with}\:{radii}\:{p},\:{q},\:{r}\:{respectively} \\ $$$${touch}\:{each}\:{other}\:{as}\:{shown}.\:{find}\:{the}\: \\ $$$${maximum}\:{area}\:{of}\:\:{triangle}\:\Delta{ABC}…