With respect to position of two circles which of the following statements is/are correct?
1. If one circle lies completely outside the other circle,
Number of direct common tangents = 2
Number of transverse common tangents = 2
2. If two circles touch each other externally
Number of direct common tangents = 2
Number of transverse common tangents = 1
3. If two circles touch each other internally
Number of direct common tangents = 1
Number of transverse common tangents = 0
4. If two circles intersect each other at two points
Number of direct common tangents = 2
Number of transverse common tangents = 0
5. If one circle lies completely inside the other circle
Number of direct common tangents = 0
Number of transverse common tangents = 0
With respect to position of two circles which of the following statements is/are correct?
1. If one circle lies completely outside the other circle,
Number of direct common tangents = 2
Number of transverse common tangents = 2
2. If two circles touch each other externally
Number of direct common tangents = 2
Number of transverse common tangents = 1
3. If two circles touch each other internally
Number of direct common tangents = 1
Number of transverse common tangents = 0
4. If two circles intersect each other at two points
Number of direct common tangents = 2
Number of transverse common tangents = 0
5. If one circle lies completely inside the other circle
Number of direct common tangents = 0
Number of transverse common tangents = 0
The correct option is D All 1, 2, 3, 4, 5
1. If one circle lies completely outside the other circle.
Definition of direct common tangent: If with respect to a tangent both the circles lie on the same side, this tangent is called direct common tangent. Here line 1 and 2 are direct common tangent. Number of direct common tangent = 2
Definition of transverse common tangent: If with respect to a tangent both the circles lie on the opposite side, this tangent is called transverse common tangent. Here, line 3 & 4 are transverse common tangent. Number of transverse common tangent = 2
By definition of direct and transverse tangents here line (1) and (2) are direct tangent and line 3 is transverse tangent.
Number of direct common tangents = 2
Number of transverse common tangents = 1
3. If two circles touch each other internally
By definition of direct and transverse common tangents, here, line (1) is a direct common tangent.
Number of direct common tangents = 1
Number of transverse common tangents = 0
4. If two circles intersect each other at two points
Here, line (1) and (2) are direct common tangents
Number of direct common tangents = 2
Number of transverse common tangents = 0
5. If one circle lies completely inside the other circle
We can see that there No common tangent
Number of direct and transverse common tangents = 0
So, all 1, 2, 3, 4 and 5 statements are correct.
2. If two circles touch each other externally
All 1, 2, 3, 4, 5
1. If one circle lies completely outside the other circle.
Definition of direct common tangent: If with respect to a tangent both the circles lie on the same side, this tangent is called direct common tangent. Here line 1 and 2 are direct common tangent. Number of direct common tangent = 2
Definition of transverse common tangent: If with respect to a tangent both the circles lie on the opposite side, this tangent is called transverse common tangent. Here, line 3 & 4 are transverse common tangent. Number of transverse common tangent = 2
By definition of direct and transverse tangents here line (1) and (2) are direct tangent and line 3 is transverse tangent.
Number of direct common tangents = 2
Number of transverse common tangents = 1
3. If two circles touch each other internally
By definition of direct and transverse common tangents, here, line (1) is a direct common tangent.
Number of direct common tangents = 1
Number of transverse common tangents = 0
4. If two circles intersect each other at two points
Here, line (1) and (2) are direct common tangents
Number of direct common tangents = 2
Number of transverse common tangents = 0
5. If one circle lies completely inside the other circle
We can see that there No common tangent
Number of direct and transverse common tangents = 0
So, all 1, 2, 3, 4 and 5 statements are correct.
2. If two circles touch each other externally
