MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Radical Axis

Three circles...

Question

Three circles touch one another externally. The tangents at their points of contact meet at a point whose distance from a point of contact is $4$ . Then the ratio of the area of triangle formed by centers to the sum of the radii of the circles is

Open in App

Solution

Let $C_{1}, C_{2}$ and $C_{3}$ be the centres of three circles of radii $r_{1}, r_{2}$ and $r_{3}$ respectively, then the length, then

From above figure in $△ C_{1} C_{2} C_{3}$
$C_{1} C_{2} = r_{1} + r_{2}, C_{2} C_{3} = r_{2} + r_{3}, C_{1} C_{3} = r_{1} + r_{3}$

Now, area of the trianlge $△ C_{1} C_{2} C_{3}$
$= Area of (△ O C_{2} C_{3} + △ O C_{1} C_{3} + △ O C_{1} C_{2})$
as $O P = O Q = O R = 4$
$∴ Area of △ C_{1} C_{2} C_{3} = 4 (r_{1} + r_{2} + r_{3})$

Suggest Corrections

thumbs-up

1

Similar questions

Q. Three circles touch one another externally. If the tangents at their points of contact meet at a point whose distance from a point of contact is

4

, then the ratio to the sum of the radii of the circles, is

Q. Three circles touch one another externally. The tangents at their points of contact meet at a point whose distance from a point of contact is

4

. Then the ratio of the product of the radii to the sum of the radii of the circles is

Q. Three circles with different radii touch one another externally. The tangents at their points of contact meet at a point whose distance from a point of contact is

4

where ratio of the product of the radii to the sum of the radii of circles is

λ^{2} : 1

. Then the value of

| λ |

Q. Three circles with radii

a, b, c

touch one another externally. If the tangents at contact points meet at point

I,

then the distance of

I

to the contact point of any two circles is:

Q. Three circles, whose radii are

a, b, c

touch each other externally and the tangents at their points of contact meet in a point. Then, the distance of this point from either of points of contact is

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Radical Axis of Two Circles

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon