Question Number 17692 by b.e.h.i.8.3.417@gmail.com last updated on 09/Jul/17 Answered by Tinkutara last updated on 09/Jul/17 Commented by b.e.h.i.8.3.417@gmail.com last updated on 09/Jul/17 $${thanks}\:{sir}.{nice}\:{and}\:{smart}. \\…
Question Number 148739 by Tawa11 last updated on 30/Jul/21 Commented by Tawa11 last updated on 30/Jul/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle}\:\:\:\:\:\:\:\mathrm{JSMT} \\ $$ Commented by Tawa11 last updated on…
Question Number 17653 by 1kanika# last updated on 09/Jul/17 $$\mathrm{A}\:\mathrm{line}\:\mathrm{segment}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{the}\:\mathrm{plane} \\ $$$$\mathrm{with}\:\mathrm{its}\:\mathrm{end}\:\mathrm{points}\:\mathrm{on}\:\mathrm{the}\:\mathrm{coordinate} \\ $$$$\mathrm{axes}\:\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{length} \\ $$$$\mathrm{of}\:\mathrm{its}\:\mathrm{intersect}\:\mathrm{on}\:\mathrm{the}\:\mathrm{coordinate}\: \\ $$$$\mathrm{axes}\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{C}\:. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{the}\:\mathrm{mid}\:\mathrm{points}\:\mathrm{of} \\ $$$$\mathrm{this}\:\mathrm{segment}\:. \\ $$$$\mathrm{Ans}.\:\mathrm{is}\:\:\:\mathrm{8}\left(\mid\mathrm{x}\mid^{\mathrm{3}} +\mid\mathrm{y}\mid^{\mathrm{3}}…
Question Number 17645 by Tinkutara last updated on 09/Jul/17 $$\mathrm{Suppose}\:\mathrm{that}\:\mathrm{the}\:\mathrm{point}\:{M}\:\mathrm{lying}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{interior}\:\mathrm{of}\:\mathrm{the}\:\mathrm{parallelogram}\:{ABCD}, \\ $$$$\mathrm{two}\:\mathrm{parallels}\:\mathrm{to}\:{AB}\:\mathrm{and}\:{AD}\:\mathrm{are}\:\mathrm{drawn}, \\ $$$$\mathrm{intersecting}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:{ABCD}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{points}\:{P},\:{Q},\:{R},\:{S}\:\left(\mathrm{See}\:\mathrm{Figure}\right).\:\mathrm{Prove} \\ $$$$\mathrm{that}\:{M}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{diagonal}\:{AC}\:\mathrm{if}\:\mathrm{and} \\ $$$$\mathrm{only}\:\mathrm{if}\:\left[{MRDS}\right]\:=\:\left[{MPBQ}\right]. \\ $$ Commented…
Question Number 17614 by Tinkutara last updated on 08/Jul/17 $$\mathrm{The}\:\mathrm{triangle}\:\mathrm{ABC}\:\mathrm{has}\:\mathrm{CA}\:=\:\mathrm{CB}.\:\mathrm{P}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{circumcircle}\:\mathrm{between}\:\mathrm{A} \\ $$$$\mathrm{and}\:\mathrm{B}\:\left(\mathrm{and}\:\mathrm{on}\:\mathrm{the}\:\mathrm{opposite}\:\mathrm{side}\:\mathrm{of}\:\mathrm{the}\right. \\ $$$$\left.\mathrm{line}\:\mathrm{AB}\:\mathrm{to}\:\mathrm{C}\right).\:\mathrm{D}\:\mathrm{is}\:\mathrm{the}\:\mathrm{foot}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{perpendicular}\:\mathrm{from}\:\mathrm{C}\:\mathrm{to}\:\mathrm{PB}.\:\mathrm{Show}\:\mathrm{that} \\ $$$$\mathrm{PA}\:+\:\mathrm{PB}\:=\:\mathrm{2}\centerdot\mathrm{PD}. \\ $$ Commented by b.e.h.i.8.3.417@gmail.com…
Question Number 17580 by b.e.h.i.8.3.417@gmail.com last updated on 08/Jul/17 Commented by b.e.h.i.8.3.417@gmail.com last updated on 08/Jul/17 $${triangle}\:{ABC},{is}\:{given}\:{with}: \\ $$$${AB}={c},{BC}={a},{AC}={b} \\ $$$${red}\:\:{lines},{are}\:{perpendicular}\:{bisectors} \\ $$$${of}\:{sides}. \\ $$$$\left.\mathrm{1}\right){find}\:{radius}\:{of}\:{a}\:{circle}\:{that}\:{passes}…
Question Number 83102 by ajfour last updated on 28/Feb/20 Commented by ajfour last updated on 28/Feb/20 $$\mathrm{Find}\:\mathrm{side}\:\boldsymbol{\mathrm{s}}\:\mathrm{of}\:\mathrm{largest}\:\mathrm{equilateral} \\ $$$$\bigtriangleup\mathrm{ABC}\:\mathrm{whose}\:\mathrm{vertices}\:\mathrm{lie}\:\mathrm{on} \\ $$$$\mathrm{three}\:\mathrm{circles}\:\mathrm{of}\:\mathrm{radii}\:\mathrm{p},\mathrm{q},\mathrm{r}\:\mathrm{touching} \\ $$$$\mathrm{each}\:\mathrm{other}\:\mathrm{externally}. \\ $$…
Question Number 17524 by 786 last updated on 07/Jul/17 $$\mathrm{The}\:\mathrm{circle}\:\omega\:\mathrm{touches}\:\mathrm{the}\:\mathrm{circle}\:\Omega \\ $$$$\mathrm{internally}\:\mathrm{at}\:{P}.\:\mathrm{The}\:\mathrm{centre}\:{O}\:\mathrm{of}\:\Omega\:\mathrm{is} \\ $$$$\mathrm{outside}\:\omega.\:\mathrm{Let}\:{XY}\:\mathrm{be}\:\mathrm{a}\:\mathrm{diameter}\:\mathrm{of}\:\Omega \\ $$$$\mathrm{which}\:\mathrm{is}\:\mathrm{also}\:\mathrm{tangent}\:\mathrm{to}\:\omega.\:\mathrm{Assume} \\ $$$${PY}\:>\:{PX}.\:\mathrm{Let}\:{PY}\:\mathrm{intersect}\:\omega\:\mathrm{at}\:{Z}.\:\mathrm{If} \\ $$$${YZ}\:=\:\mathrm{2}{PZ},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of} \\ $$$$\angle{PYX}\:\mathrm{in}\:\mathrm{degrees}? \\ $$ Answered…
Question Number 17520 by 1kanika# last updated on 07/Jul/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{coordinate}\:\mathrm{of}\:\mathrm{the}\:\mathrm{point}\:\mathrm{in} \\ $$$$\mathrm{R}\Lambda\mathrm{3}\:\mathrm{which}\:\mathrm{is}\:\mathrm{the}\:\mathrm{reflection}\:\mathrm{the}\:\mathrm{point} \\ $$$$\left(\mathrm{1},\mathrm{2},\mathrm{3}\right)\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to}\:\mathrm{plane}\: \\ $$$$\mathrm{X}+\mathrm{Y}+\mathrm{Z}=\mathrm{1}\:. \\ $$ Commented by 1kanika# last updated on 07/Jul/17…
Question Number 83032 by Power last updated on 27/Feb/20 Answered by mr W last updated on 27/Feb/20 Commented by mr W last updated on 27/Feb/20…