geometry

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True or false
Tangent circles always have exactly one common tangent.

  • geometry -

    False. Draw two tangent circles.

    If one is not inside the other, then there is a tangent line that passes between the circles, touching each at the point of tangency.

    There are also two lines that lie outside the circles, but lean up against both of them. Those are also common tangents.

    If one circle is inside the other, then there is just a single common tangent.

  • geometry -

    If the area of a rectangle is 50cm and two circles are inside which are tangent to each other and the rectangle's side. What is the radius?

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