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Category: Geometry

Question-53664

Question Number 53664 by ajfour last updated on 24/Jan/19 Commented by ajfour last updated on 24/Jan/19 $${The}\:{bases}\:{of}\:{the}\:{cones}\:{touch}\:{each} \\ $$$${other}\:{pairwise}.\:{Find}\:{the}\:{radius}\:{of} \\ $$$${the}\:{sphere}\:{tangent}\:{to}\:{all}\:{the}\:{three} \\ $$$${cones}\:{and}\:{to}\:{the}\:{plane}\:{passing} \\ $$$${through}\:{their}\:{vertices}.\:\left({semi}-{vertical}\right.…

Question-184718

Question Number 184718 by sonukgindia last updated on 10/Jan/23 Answered by HeferH last updated on 10/Jan/23 $${Let}\:\mathrm{2}{a}\:{be}\:{the}\:{side}\:{of}\:{those}\:{squares}\:{and}\:{x}\:{the}\: \\ $$$${larger}\:{side}\:{of}\:{the}\:{yellow}\:{triangle}.\: \\ $$$$\:{A}_{{rect}} =\:\mathrm{2}{a}\:\centerdot\:\mathrm{4}{a}\:=\mathrm{8}{a}^{\mathrm{2}} \\ $$$$\:{by}\:{product}\:{of}\:{chords}: \\…