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Category: Geometry

In-a-right-triangle-the-mid-point-of-the-hypotenuse-is-equidistant-from-all-the-three-vertices-of-the-triangle-

Question Number 4579 by Rasheed Soomro last updated on 08/Feb/16 $${In}\:{a}\:{right}\:{triangle},\:{the}\:{mid}-{point}\:{of}\:{the} \\ $$$${hypotenuse}\:{is}\:{equidistant}\:{from}\:{all}\:{the} \\ $$$${three}\:{vertices}\:{of}\:{the}\:{triangle}. \\ $$ Commented by Yozzii last updated on 08/Feb/16 $${Prove}\:{this}\:{theorem}?…

Triangle-ABC-has-midpoints-D-E-and-F-By-connecting-each-verticie-with-the-opposite-midpoint-we-create-a-cress-section-called-G-Prove-that-all-three-lines-cross-at-point-G-regardless-of-the-type

Question Number 4543 by FilupSmith last updated on 06/Feb/16 $$\mathrm{Triangle}\:{ABC}\:\mathrm{has}\:\mathrm{midpoints} \\ $$$${D},\:{E}\:\mathrm{and}\:{F}. \\ $$$$ \\ $$$$\mathrm{By}\:\mathrm{connecting}\:\mathrm{each}\:\mathrm{verticie}\:\mathrm{with}\:\mathrm{the} \\ $$$$\mathrm{opposite}\:\mathrm{midpoint},\:\mathrm{we}\:\mathrm{create}\:\mathrm{a}\:\mathrm{cress}−\mathrm{section} \\ $$$$\mathrm{called}\:{G}. \\ $$$$ \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{all}\:\mathrm{three}\:\mathrm{lines}\:\mathrm{cross}\:\mathrm{at}\: \\…

Question-4505

Question Number 4505 by Yozzii last updated on 03/Feb/16 Commented by Yozzii last updated on 03/Feb/16 $$\bigtriangleup{ACD}\:{and}\:\bigtriangleup{DBE}\:{are}\:{equilateral}. \\ $$$${F}\:{is}\:{the}\:{midpoint}\:{of}\:{AE}\:{and}\:{G}\:{is}\:{the} \\ $$$${midpoint}\:{of}\:{BC}.\:{D}\:{is}\:{a}\:{point}\:{on}\:{the} \\ $$$${line}\:{AB}.\:{Prove}\:{that}\:\bigtriangleup{FGD}\:{is}\: \\ $$$${equilateral}.\:…

This-is-a-simple-question-but-for-some-silly-reason-I-can-t-figure-it-out-1-If-I-have-a-circle-with-radius-r-and-area-A-and-I-wish-to-make-a-new-circle-with-n-times-the-area-for-what-new-value-

Question Number 4496 by FilupSmith last updated on 01/Feb/16 $$\mathrm{This}\:\mathrm{is}\:\mathrm{a}\:\mathrm{simple}\:\mathrm{question}\:\mathrm{but}\:\mathrm{for}\:\mathrm{some} \\ $$$$\mathrm{silly}\:\mathrm{reason}\:\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{figure}\:\mathrm{it}\:\mathrm{out}… \\ $$$$ \\ $$$$\mathrm{1}. \\ $$$$\mathrm{If}\:\mathrm{I}\:\mathrm{have}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{radius}\:{r}\:\mathrm{and} \\ $$$$\mathrm{area}\:{A},\:\mathrm{and}\:\mathrm{I}\:\mathrm{wish}\:\mathrm{to}\:\mathrm{make}\:\mathrm{a}\:\mathrm{new}\:\mathrm{circle}\:\mathrm{with} \\ $$$${n}\:\mathrm{times}\:\mathrm{the}\:\mathrm{area},\:\mathrm{for}\:\mathrm{what}\:\mathrm{new}\:\mathrm{value} \\ $$$$\mathrm{of}\:{r}\:\mathrm{should}\:\mathrm{be}\:\mathrm{used}? \\…

An-ellipse-having-semi-major-axis-length-a-and-semi-minor-axis-length-b-and-a-circle-having-radius-r-have-equal-area-Express-r-in-terms-of-a-and-b-

Question Number 4437 by Rasheed Soomro last updated on 25/Jan/16 $$\mathrm{An}\:\boldsymbol{\mathrm{ellipse}}\:\mathrm{having}\:\boldsymbol{\mathrm{semi}}-\boldsymbol{\mathrm{major}}\:\boldsymbol{\mathrm{axis}}\: \\ $$$$\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{a}}\:\:\mathrm{and}\:\boldsymbol{\mathrm{semi}}-\boldsymbol{\mathrm{minor}}\:\boldsymbol{\mathrm{axis}}\:\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{b}} \\ $$$$\mathrm{and}\:\mathrm{a}\:\boldsymbol{\mathrm{circle}}\:\mathrm{having}\:\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{r}}\:\mathrm{have}\:\mathrm{equal} \\ $$$$\boldsymbol{\mathrm{area}}. \\ $$$$\mathrm{Express}\:\boldsymbol{\mathrm{r}}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}}. \\ $$$$ \\ $$ Answered by…