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Byju's Answer

Standard VIII

Mathematics

Length of Internal Common Tangent

If one circle...

Question

If one circle lie completely outside the other circle, P, the intersection of transverse (indirect) common tangent, lie on the line joining the centers of the two circles and divide it internally in the ratio of their radii

True

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False

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Solution

The correct option is A
True

Let $c_{1} & c_{2}$ be the centers and $r_{1} a n d r_{2}$ radii of two circles (1) and (2) respectively

Transverse (indirect) common tangent lie on the line joining the centers of the two circles and divide it internally in the ratio of $r_{1} : r_{2} .$

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Similar questions

If one circle lie completely outside the other circle, P, the intersection of transverse (indirect) common tangent, lie on the line joining the centers of the two circles and divide it internally in the ratio of their radii

If one circle lie completely outside the other circle, Q , the intersection of direct common tangent, lie on the line joining the centers of the two circles and divide it internally in the ratio of their radii.

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

Length of internal (transverse) common tangent to two circles is $L_{i n t} = \sqrt{d^{2} - (r_{1} - r_{2})^{2}}$

Where d = distance between the centers of the two circles $r_{1} & r_{2}$ are radii of two circles

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If one circle lie completely outside the other circle, P, the intersection of transverse (indirect) common tangent, lie on the line joining the centers of the two circles and divide it internally in the ratio of their radii

The correct option is A True Let c1 & c2 be the centers and r1 and r2 radii of two circles (1) and (2) respectively Transverse (indirect) common tangent lie on the line joining the centers of the two circles and divide it internally in the ratio of r1:r2.

The correct option is A
True

Let $c_{1} & c_{2}$ be the centers and $r_{1} a n d r_{2}$ radii of two circles (1) and (2) respectively

Transverse (indirect) common tangent lie on the line joining the centers of the two circles and divide it internally in the ratio of $r_{1} : r_{2} .$