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1.Common tangents: –
Common Tangents: – The lines that touch two circles are called common tangents.
d → distance between the centre of two circle.
a) If two circles touch each other externally, then the number of common tangents drawn on them is three. (d = R + r)
d → distance
b) If two circles do not touch each other, then the number of common tangents is four
(d > R + r)
c) If two circle touch each other internally, then the number of common tangents drawn on them is only one.
d) If two circles intersects each other, then the number of common tangents drawn on them is only 2.
e) Only two tangents can be drawn on the circle from a point outside it.
2. The line segment joining the centre of a circle to the mid-point of its chord is perpendicular to that chord.
3. Through three non-collinear points, there passes only one circle.
4. The chords of a circle which are equidistant from the centre of a circle are equal.
5. The angle subtended by an arc at the centreis double the angle subtended by it at any point on the remaining part of the circle.
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