Can anyone help me

$P,Q,R,S$ 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

#Geometry

Easy Math Editor

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Comments

@Nihar mahajan , @cheo-sheong cheong help

anish raj - 5 years, 2 months ago

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

Indraneel Mukhopadhyaya - 5 years, 2 months ago

Those are notation of “triange”.

anish raj - 5 years, 2 months ago

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.

Indraneel Mukhopadhyaya - 5 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$