We have a circle x^2 + y^2 = R^2. And a smaller circle touches it internally at point (-R,0). The smaller circle cuts X and Y axis at points (R-6,...?

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We have a circle x^2 + y^2 = R^2. And a smaller circle touches it intern…

Mathematics for School & Entrance Level • 1.5K followers This space shows mathematics, suitable for school & Engineering Entrance Exam.   We have a circle x^2 + y^2 = R^2. And a smaller circle touches it internally at point (-R,0). The smaller circle cuts X and Y axis at points (R-6, 0) and (0, R-4) respectively. Is it possible to know the value of R now? If you have got 'R' then please tell the radius of smaller circle also. Dave Benson, trying to make maths easy. Answered March 29   We have a circle x^2 + y^2 = R^2. And a smaller circle touches it internally at point (-R,0). The smaller circle cuts X and Y axis at points (R-6, 0) and (0, R-4) respectiv... Read more »     If two roots of equation x²-8x +2=0, are 'm' and 'n', then what is the value of (1/m² + 1/n²)? Gary Russell, Professor Emeritus, University of Iowa Answered Wed   According to the Fundamental Theorem of Algebra, the quadratic in the question can be written as f(x) = (x-m)(x-n) = x^2 - (m+n)x + mn We know immediately that m + n = 8... Read more »     If f (2x+1) = 6x, then f(x) =? Enrico Gregorio, Associate professor in Algebra Answered 20h ago   I guess the question is missing “for all [math]x[/math]”. If in doubt, change variable: [math]f(2y+1)=6y[/math] Now set [math]x=2y+1,[/math] whereby [math]y=(x-1)/2[/math] and so [math]f(x)=6\cdot\dfrac{x-1}{2}=3x-3[/math] Read more »   Read more in Mathematics for School & Entrance Level

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