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Byju's Answer

Standard VI

Mathematics

Right, Straight and Complete Angles

A B are c...

Question

$A$ & $B$ are centres of circles of radii $9$ cm and $2$ cm respectively. $A B = 17 c m$ . $R$ is the center of the circle of radius $x c m$ which touches the above circle externally. Given that angle $A R B$ is $90^{o}$ . Write an equation in $x$ and solve it.

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Solution

REF.Image
In $△ A R B$ , by Pythagoras theorem
$A B^{2} = A R^{2} + R B^{2}$
$17^{2} = (x + 9)^{2} + (x + 2)^{2}$
$289 = x^{2} + 81 + 18 x + x^{2} + 4 + 4 x$
$289 = 2 x^{2} + 22 x + 85$
$2 x^{2} + 22 x - 204 = 0$
$x^{2} + 11 x - 102 = 0$
$x^{2} + 17 x - 6 x - 102 = 0$
$x (x + 17) + 6 (x + 17) = 0$
$(x + 17) (x - 6) = 0$
$x = 6, - 17$
$∴ x = 6$ as cannot be negative

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A & B are centres of circles of radii 9cm and 2cm respectively. AB=17 cm. R is the center of the circle of radius x cm which touches the above circle externally. Given that angle ARB is 90o. Write an equation in x and solve it.

REF.ImageIn △ARB, by Pythagoras theoremAB2=AR2+RB2172=(x+9)2+(x+2)2289=x2+81+18x+x2+4+4x289=2x2+22x+852x2+22x−204=0x2+11x−102=0x2+17x−6x−102=0x(x+17)+6(x+17)=0(x+17)(x−6)=0x=6,−17∴x=6 as cannot be negative

$A$ & $B$ are centres of circles of radii $9$ cm and $2$ cm respectively. $A B = 17 c m$ . $R$ is the center of the circle of radius $x c m$ which touches the above circle externally. Given that angle $A R B$ is $90^{o}$ . Write an equation in $x$ and solve it.