Bob
]]>This one shows a circle in the middle (B) and one on the left that crosses it (A) and one on the right that just touches it (C) .
The tangent to B where it crosses A cuts A again.
The tangent to B where it touches C is also a tangent for C.
General rule. When two circles touch they share a common tangent.
A tangent is always at right angles to the radius at the point where the tangent touches.
So back to the previous diagram:
ABC = 90. If you give a letter to a fourth point, you'll complete a square. So BC = r
And AD is perpendicular to the common tangent at D (haven't drawn this line) and DC is too.
So ADC is a straight line.
Bob
]]>But what if the examiner asks me How do I know that BC = r (apart from intution)?
]]>See diagram. Let the radius of the little circle be R
AB = BC = r
AC = R + r (why?)
So you should be able to use Pythagoras here.
Bob
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