practice problems pending

 1. Show that length of direct common tangent of 2 non intersecting circles(touching is fine) is sqrt(d^2 - (r1-r2)^2) and that of the transverse tangent is sqrt(d^2 - (r1+r2)^2) where 'd' is the distance between the centers of those 2 circles.

2. Now show that if the 2 circles touch each other than DCT length = 2.sqrt(r1r2).

3. If two circles with radii (a) and (b) touch each other externally. Let (c) be the radius of a circle that touches these two circles as well as a common tangent of these two circles. Prove

1/sqrt(c) = 1/sqrt(a) + 1/sqrt(b)

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