Can anyone help me

P,Q,R,SP,Q,R,S are the centres of the four circles each of which is cut by a fixed circle orthogonally. If I12,I22,I32,I42I^{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.a. I12ΔQRSI22ΔRSP+I32ΔSPQI42ΔPQR=0I^{2}_1\Delta QRS-I^{2}_2\Delta RSP+I^{2}_3\Delta SPQ-I^{2}_4\Delta PQR=0

b.b. I12ΔQRS+I22ΔRSPI32ΔSPQ+I42ΔPQR=0I^{2}_1\Delta QRS+I^{2}_2\Delta RSP-I^{2}_3\Delta SPQ+I^{2}_4\Delta PQR=0

c.c. I12ΔQRSI22ΔRSP+I32ΔSPQI42ΔPQR=1I^{2}_1\Delta QRS-I^{2}_2\Delta RSP+I^{2}_3\Delta SPQ-I^{2}_4\Delta PQR=-1

d.d. none of these

Note by Anish Raj
5 years ago

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@Nihar mahajan , @cheo-sheong cheong help

anish raj - 5 years ago

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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”.

anish raj - 5 years ago

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Even I know that.What I want to ask is what do we mean by I12I1^2triangle QRS.Does it mean square of tangent length from a fixed point to circumcircle of triangle QRS.

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