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MATH / A square region ABCD is externally tangent to the circle with equation x²+y²=1 at the point (0,1) on the side CD. Vertices A and B are on the circle with equation x²+y²=4. The side…

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problem

A square region ABCDABCD is externally tangent to the circle with equation x2+y2=1x^2+y^2=1 at the point (0,1)(0,1) on the side CDCD. Vertices AA and BB are on the circle with equation x2+y2=4x^2+y^2=4. The side length of this square can be expressed in the form ab−cd\frac{a\sqrt{b}-c}{d}, where bb is not divisible by the square of any prime, and aa, cc, and dd share no common factors. Find a+b+c+da+b+c+d.
Plain-text mathematical notation (without MathML)
A square region ABCD is externally tangent to the circle with equation x²+y²=1 at the point (0,1) on the side CD.  Vertices A and B are on the circle with equation x²+y²=4.  The side length of this square can be expressed in the form (a√(b)−c)/(d), where b is not divisible by the square of any prime, and a, c, and d share no common factors. Find a+b+c+d.
Original LaTeX notation
A square region $ABCD$ is externally tangent to the circle with equation $x^2+y^2=1$ at the point $(0,1)$ on the side $CD$.  Vertices $A$ and $B$ are on the circle with equation $x^2+y^2=4$.  The side length of this square can be expressed in the form $\frac{a\sqrt{b}-c}{d}$, where $b$ is not divisible by the square of any prime, and $a$, $c$, and $d$ share no common factors. Find $a+b+c+d$.

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
4450be28-4a4f-5cb5-ac8f-f44384ac804e
task_key
intermediate~5falgebra--test--4450be28-4a4f-5cb5-ac8f-f44384ac804e
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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