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Standard X

Mathematics

Length of External Common Tangent

If one circle...

Question

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.

True

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False

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Solution

The correct option is B
False

Let's draw two circles which neither intersect nor touch. Let $c_{1} & c_{2}$ be centers and $r_{1}$ and $r_{2}$ radii.

Direct common tangent lie on the line joining the centers of the two circles and divide it externally in the ratio of $r_{1} : r_{2}$ So, given statement is wrong.

Suggest Corrections

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

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

Statement:-

| z | \geq 3,

the points z lie outside and on the circle whose center is origin and radius unity.

Is it True or False?

If two circles intersect at two points, then prove that their centers lie on the perpendicular bisector of the common chord. [2 MARKS]

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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.

The correct option is B False Let's draw two circles which neither intersect nor touch. Let c1 & c2 be centers and r1 and r2 radii. Direct common tangent lie on the line joining the centers of the two circles and divide it externally in the ratio of r1:r2 So, given statement is wrong.