Menu Close

Category: Coordinate Geometry

prove-that-9pi-8-9-4-sin-1-1-3-9-4-sin-1-2-2-3-

Question Number 44480 by peter frank last updated on 29/Sep/18 $${prove}\:{that}\:\:\frac{\mathrm{9}\pi}{\mathrm{8}\:\:}−\frac{\mathrm{9}}{\mathrm{4}}\mathrm{sin}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{3}}=\frac{\mathrm{9}}{\mathrm{4}}\mathrm{sin}^{−\mathrm{1}} \frac{\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{3}} \\ $$ Answered by math1967 last updated on 30/Sep/18 $${L}.{H}.{S}=\frac{\mathrm{9}}{\mathrm{4}}\left(\frac{\pi}{\mathrm{2}}−\mathrm{sin}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{3}}\right) \\…

The-equations-of-the-sides-AC-BC-and-AB-of-a-right-angled-triangled-with-lengths-a-b-and-c-are-y-7-x-11-and-4x-3y-5-0-respectively-Find-the-equation-of-the-inscribed-circle-of-the-triangle-i

Question Number 175237 by nadovic last updated on 24/Aug/22 $$\mathrm{The}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sides}\:\:\mathrm{AC},\:\mathrm{BC} \\ $$$$\mathrm{and}\:\mathrm{AB}\:\mathrm{of}\:\:\mathrm{a}\:\mathrm{right}−\mathrm{angled}\:\mathrm{triangled} \\ $$$$\mathrm{with}\:\mathrm{lengths}\:{a},\:{b}\:\mathrm{and}\:{c}\:\mathrm{are}\:{y}\:=\:−\mathrm{7}, \\ $$$${x}=\mathrm{11}\:\mathrm{and}\:\mathrm{4}{x}−\mathrm{3}{y}−\mathrm{5}=\mathrm{0}\:\mathrm{respectively}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{inscribed} \\ $$$$\mathrm{circle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle},\:\mathrm{if}\:\mathrm{its}\:\mathrm{radius}\:{r}, \\ $$$$\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:{r}\:=\:\frac{{a}+{b}−{c}}{\mathrm{2}}. \\ $$ Terms…

Question-44088

Question Number 44088 by peter frank last updated on 21/Sep/18 Answered by $@ty@m last updated on 21/Sep/18 $$\left(\boldsymbol{{a}}\right)\:\angle{BCA}=\angle{BCD}\:\left({same}\:{angle}\right) \\ $$$$\angle{ABC}=\angle{BDC}\:\left({right}\:{angle}\right) \\ $$$$\angle{BAC}=\angle{DBC}\:\left({third}\:{angle}\right) \\ $$$$\therefore\bigtriangleup{ABC}\sim\bigtriangleup{BDC} \\…