when do we say that 2 circles intersect ortogonally?

Question

apoorvk · Answer

There is this general criteria that for the standard equation of two circles S_1 and S_2

$$(Standard ~equation = x^2 + y^2 + 2gx + 2fy +c = 0)$$

So, for orthogonal circles,
$$\large 2(g_1g_2 + f_1f_2) = c_1 + c_2$$

aravindg · Answer

can u say what we mean by orthogonal intersection ?

apoorvk · Answer

Orthogonal intersection means they intersect at right angles - rather the tangents to both the circles at their points of intersection are perpendicular. Like this:|dw:1338488001396:dw|

aravindg · Answer

so when all is orthogonal intersection possible?is it there when the circles just touch each other?

apoorvk · Answer

I'm sorry, I thought you were looking for the mathematical formula, initially. :P

aravindg · Answer

no prob :) u see the formula was there in my material but theory was nt xplained

apoorvk · Answer

No - try to think!

When they just 'touch' they are tangentially to one another - so there is no chance of them being orthogonal at all.

Like I said - the mathematical relation above relates if two circles intersect orthogonally.

apoorvk · Answer

Hmm, getting a 'feel' of the theory is essential ;)

aravindg · Answer

what we mean by chord of contact?

aravindg · Answer

|dw:1338488685784:dw| do these 4 lines form a square or rectangle ?