\(P,Q,R,S\) are the centres of the four circles each of which is cut by a fixed circle orthogonally. If \(I^{2}_1,I^{2}_2,I^{2}_3,I^{2}_4\) are the squares of length of tangents to the four circles from a point in their plane then

\(a.\) \(I^{2}_1\Delta QRS-I^{2}_2\Delta RSP+I^{2}_3\Delta SPQ-I^{2}_4\Delta PQR=0\)

\(b.\) \(I^{2}_1\Delta QRS+I^{2}_2\Delta RSP-I^{2}_3\Delta SPQ+I^{2}_4\Delta PQR=0\)

\(c.\) \(I^{2}_1\Delta QRS-I^{2}_2\Delta RSP+I^{2}_3\Delta SPQ-I^{2}_4\Delta PQR=-1\)

\(d.\) none of these

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TopNewest@Nihar mahajan , @cheo-sheong cheong help

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Could you explain the notation that you have used in the first three options?

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Those are notation of “triange”.

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Even I know that.What I want to ask is what do we mean by \(I1^2\)triangle QRS.Does it mean square of tangent length from a fixed point to circumcircle of triangle QRS.

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