Transverse Common Tangent
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If is the tangent to a circle with centre , then the other tangent drawn through to the circle is
Let c1& c2 be the centers and r1& r2 be the radius of two circles. Then
Cases Conditions
p. 1.|r1−r2|< c1c2< r1+r2
q. 2. |r1−r2|=c1c2
r. 3.c1c2< |r1+r2|
s.
4. r1+r2< c1r2
t. 5. r1+r2=c1r2
p - 5, q - 4 , r - 1, s - 2 , t - 3
p - 4, q - 5 , r - 1, s - 3 , t - 2
p - 1, q - 2 , r - 3, s - 4 , t - 5
p - 4, q - 5 , r - 1 , s - 2 , t - 3
Let C be the circle with centre at (1, 1) and radius 1. If T is the circle centred at (0, y) passing through origin and touching the circle C externally, then the radius of T is equal to
12
14
√3√2
√32
Find the Slope of the transverse common tangent to the circles x2 + y2 − 4x + 6y − 12 = 0 and x2 + y2 + 6x + 18y + 26 = 0
−512
512
125
−125