Circle: Common Tangents

Family Of Circles|Common Tangents to Two Circles|OMR

Illustrations Based On Chord OF Contact Power OF Point || Relative Position OF two Circles and Common Tangents

Suppose S_(1)" and "S_(2) are two unequal circles, AB and CD are the direct common tangents to these circles. A transverse common tangent PQ cuts AB in R and CD in S. If AB = 10, then RS is -

There are two identical circles of radius 10 cm each. If the length of the direct common tangent is 26 cm, then what is the length (in cm) of the transverse common tangent?

Statement 1 : The number of common tangents to the circles x^(2) +y^(2) -x =0 and x^(2) +y^(2) +x =0 is 3. Statement 2 : If two circles touch each other externally then it has two direct common tangents and one indirect common tangent.

Statement 1 : The number of common tangents to the circles x^(2) + y^(2) =4 and x^(2) + y^(2) -6x - 6y = 24 is 3. Statement 2 : If two circles touch each other externally thenit has two direct common tangents and one indirect common tangent.

The point of intersection of direct common tangents and transverse common tangents to two circles divide the line segmenta joining the two centres externally and internally respectively in the ratio of their radii.

In the diagram above, A,B,P and Q are points of contacts of direct common tangents of the two circles. If angle ACB is 120^@ , then find the angle between the two tangents and angle made by PQ at the centre of same circle.

Give two circles intersecting orthogonally having the length of common chord 24//5 units. The radius of one of the circles is 3 units. The angle between direct common tangents is