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Standard XII

Mathematics

Normal

The radii of ...

Question

The radii of two circles are $2$ units and $3$ units. lf the radical axis of the circles cuts one of the common tangents of the circle in $P$ then ratio in which $P$ divides the common tangent is

2 : 3

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3 : 2

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4 : 9

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1 : 1

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Solution

The correct option is D $1 : 1$
Radius axis is the locus of point from which equal length of tangents are drawn to two given circles.
$∴$ Length of tangents are equal.
We know, $P A = P B$
So, common tangent is divided in $1 : 1$ ratio.

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Similar questions

Q. Let two circles touch each other externally and

P

is the point of intersection of there direct common tangents. If the direct common tangents from

P

touches the circles at

A

and

B

on same side and

P A = A B = 4

, then the radius of smaller circle (in units) is

Q. Two circles of radii 7 cm and 3 cm are drawn with centres M and N respectively. Their transverse common tangents meet MN in P, then the point P divides MN (internally) in the ratio

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

Q. Let two circles touch each other externally and

P

is the point of intersection of there direct common tangents. If the direct common tangents from

P

touches the circles at

A

and

B

on same side and

P A = A B = 4

, then the radius of smaller circle (in units) is

Q. lf

S_{1} = 0, S_{2} = 0

and

S_{3} = 0

are the three circles whose radical centre is the point

P

, then the lengths

l_{1}, l_{2}, l_{3}

of the tangent from

P

to the three circles are such that

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The radii of two circles are 2 units and 3 units. lf the radical axis of the circles cuts one of the common tangents of the circle in P then ratio in which P divides the common tangent is

The correct option is D 1:1Radius axis is the locus of point from which equal length of tangents are drawn to two given circles.∴ Length of tangents are equal.We know, PA=PBSo, common tangent is divided in 1:1 ratio.

The radii of two circles are $2$ units and $3$ units. lf the radical axis of the circles cuts one of the common tangents of the circle in $P$ then ratio in which $P$ divides the common tangent is

The correct option is D $1 : 1$
Radius axis is the locus of point from which equal length of tangents are drawn to two given circles.
$∴$ Length of tangents are equal.
We know, $P A = P B$
So, common tangent is divided in $1 : 1$ ratio.