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tmua.me Extreme Set A Paper 1 · Q2

Paper 1Geometry

The circles CC and DD have equations

C: x2+y2=1,D: (x−3)2+y2=1.C:\ x^2+y^2=1,\qquad D:\ (x-3)^2+y^2=1.

A point PP moves once around DD. The two tangents from PP to CC meet CC at AA and BB, and MM is the midpoint of ABAB.

What is the area enclosed by the curve traced by MM?

Diagram for question 2

One possible position of P is shown.

Aπ256\dfrac{\pi}{256}
Bπ64\dfrac{\pi}{64}
Cπ16\dfrac{\pi}{16}
Dπ8\dfrac{\pi}{8}
Eπ4\dfrac{\pi}{4}
Fπ\pi

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