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Category: Mensuration

Question-19915

Question Number 19915 by ajfour last updated on 18/Aug/17 Commented by ajfour last updated on 18/Aug/17 $${Four}\:{equal}\:{spheres}\:{of}\:{radius}\:{r} \\ $$$${are}\:{externally}\:{tangent}\:{to}\:{the}\:{three} \\ $$$${others}.\:{Find}\:{the}\:{radius}\:{of}\:{a}\:{sphere} \\ $$$${tangent}\:{to}\:{all}\:{four}\:{spheres}\:{and} \\ $$$${containing}\:{them}\:{within}\:{it}.…

Question-19912

Question Number 19912 by ajfour last updated on 17/Aug/17 Commented by ajfour last updated on 18/Aug/17 $${Find}\:{tangent}\:{of}\:{the}\:{acute}\:{angle} \\ $$$${between}\:{AB}\:{and}\:{SC}\:{and}\:{the} \\ $$$${shortest}\:{distance}\:{between}\:{them}. \\ $$$${The}\:{side}\:{of}\:{the}\:{equilateral}\:{triangle} \\ $$$${is}\:{even}\:\boldsymbol{{a}}.\:{SA}\:{is}\:{perpendicular}\:{to}…

Question-19736

Question Number 19736 by ajfour last updated on 15/Aug/17 Commented by ajfour last updated on 15/Aug/17 $$\mathrm{Q}.\mathrm{19699}\:\:\:\left(\mathrm{solution}\right) \\ $$$$\mathrm{Find}\:\mathrm{r}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{R}\:\left(=\mathrm{100}\right) \\ $$$$\angle\mathrm{OXY}=\mathrm{30}°\:. \\ $$ Answered by…

Question-19675

Question Number 19675 by ajfour last updated on 14/Aug/17 Commented by ajfour last updated on 14/Aug/17 $$\mathrm{Q}.\mathrm{19668}\:\mathrm{Find}\:\mathrm{r}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{side}\:\boldsymbol{\mathrm{d}} \\ $$$$\mathrm{of}\:\mathrm{equilareral}\:\bigtriangleup\mathrm{ABC}\:. \\ $$ Answered by ajfour last…

Prove-that-the-radius-of-a-circle-passing-through-the-midpoints-of-the-sides-of-a-triangle-ABC-is-half-the-radius-of-a-circle-circum-scribed-about-the-triangle-

Question Number 19610 by ajfour last updated on 13/Aug/17 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle} \\ $$$$\mathrm{passing}\:\mathrm{through}\:\mathrm{the}\:\mathrm{midpoints} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{ABC}\:\mathrm{is} \\ $$$$\mathrm{half}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{circum}- \\ $$$$\mathrm{scribed}\:\mathrm{about}\:\mathrm{the}\:\mathrm{triangle}. \\ $$ Commented by ajfour last updated…

Given-in-an-isosceles-triangle-a-lateral-side-b-and-the-base-angle-Compute-the-distance-from-the-centre-of-the-inscribed-circle-to-the-centre-of-the-circumscribed-circle-

Question Number 19586 by ajfour last updated on 13/Aug/17 $$\mathrm{Given}\:\mathrm{in}\:\mathrm{an}\:\mathrm{isosceles}\:\mathrm{triangle}\:\mathrm{a} \\ $$$$\mathrm{lateral}\:\mathrm{side}\:\mathrm{b}\:\mathrm{and}\:\mathrm{the}\:\mathrm{base}\:\mathrm{angle}\:\alpha. \\ $$$$\mathrm{Compute}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{centre}\:\mathrm{of}\:\mathrm{the}\:\mathrm{inscribed}\:\mathrm{circle}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{centre}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circumscribed}\:\mathrm{circle}. \\ $$ Commented by Tinkutara last updated…