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MioMath 2024 Paper 1 · Q14

Paper 1GeometryAlgebra

Circle C1C_1 has the equation (x−32)2+(y−32)2=18(x-3\sqrt{2})^2+(y-3\sqrt{2})^2=18. A new circle, C2C_2, is drawn so that it passes through the point (0,32)(0,3\sqrt{2}) and is internally tangent to C1C_1. The difference between the area of C1C_1 and C2C_2 is 32π32\pi. Which of the following is an equation for C2C_2?

A(x+52)2+(y−32)2=25(x+5\sqrt{2})^2+(y-3\sqrt{2})^2=25
B(x+52)2+y2=50(x+5\sqrt{2})^2+y^2=50
C(x+42)2+(y−32)2=32(x+4\sqrt{2})^2+(y-3\sqrt{2})^2=32
Dx2+(y−32)2=18x^2+(y-3\sqrt{2})^2=18
E(x−52)2+(y−32)2=50(x-5\sqrt{2})^2+(y-3\sqrt{2})^2=50

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