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# Prove that the two circles shown below are similar.Download gif

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We have thatcircle xcenter point is (-2,8), radius r=6 unitsthe equation of a circle of x is (x+2)2+(y-8)2=62circle ycenter point (4,2)of radius r=3 unitsthe equation of a circle of x is (x-4)2+(y-2)2=32we know thatIf I can transform circle, x, circle, and using only translations, rotations, and scaling (In the case of the circles, with no rotations are necessary)thencircle x and circle and similarhencestep 1scaling circle of radius x by a factor of 0.5 r=6 units----------> r=6*0.5--------> r=3 unitsstep2translate the center of the circle x (-2,8)6 units in right6 units down(x,y)--------> (x+6,and-6)(-2,8)-------->(-2+6,8-6)--------> (-4,2)now the circle x and the circle and have the same radius from the same center using only the translation and scalingthereforecircle x a circle, and are similar