# geo6 - Problems in Geometry(6 1 What is the locus of a...

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Problems in Geometry (6) 1. What is the locus of a point whereof the power with respect to a ﬁxed circle is a constant ? 2. Compute the power of the point P ( x 0 ,y 0 ) with respect to the circle x 2 + y 2 +2 ax +2 by + c = 0 . Write down the equation of the radical axis of the circles x 2 + y 2 +2 a 1 x +2 b 1 y + c 1 = 0 and x 2 + y 2 + 2 a 2 x + 2 b 2 y + c 2 = 0 . 3. Consider ﬁxed non-concentric circles Γ 1 , Γ 2 . Prove that the locus of a point whereof the powers with respect to Γ 1 and Γ 2 diﬀer by a constant is a line parallel to the radical axis of Γ 1 and Γ 2 . 4. Prove that the locus of a point whereof the ratio of powers with respect to two given circles Γ 1 , Γ 2 is a constant is a circle the centre of which lies on the line joining centres of Γ 1 , Γ 2 . 5. Given two orthogonal circles, is it possible for the centre of one to lie on the other ? 6. Let each one of the circles C 1 , C 2 intersect each one of the circles Γ 1 , Γ 2 orthogonally. Prove that the radical axis of

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geo6 - Problems in Geometry(6 1 What is the locus of a...

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