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In the given figure, three circles with ...

In the given figure, three circles with centres `A`, `B`, `C` respectively touch each other externally. If `AB=5cm`, `BC=7cm` and `CA=6cm` then the radius of the circle with centre `A` is

A

`1.5cm`

B

`2cm`

C

`2.5cm`

D

`3cm`

Text Solution

Verified by Experts

Let the radii of the three circles be `x,y,z` respectively. Then,
`x+y=5`, `y+z=7` and `z+x=6implies2(x+y+z)=18impliesx+y+x=9`.
`:.x=(x+y+z)-(y+z)=(9-7)=2cm`.
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RS AGGARWAL-CIRCLES-Multiple-choice questions (MCQ)
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  3. In the given figure, two circles touch each other at C and AB is a tan...

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  5. In the given figure, PQR is a tangent to the circle at Q, whose centre...

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  6. In the given figure, O is the centre of a circle, BOA is its diameter ...

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  7. In the figure, a circle touches the side DF of triangle EDF at H and t...

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  8. In the figure, O is the centre of a circle,PQL and PRM are the tangent...

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  9. In the given figure, a triangle PQR is drawn to circumscribe a circle ...

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  10. In the given figure, QR is a common tangent to the given circles, touc...

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  11. In the given figure, quad. ABCD is circumscribed, touching the circle ...

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  12. In the given figure, quadrilateral ABCD is circumscribed, touching the...

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  13. In the given figure, O is the centre of a circle , AB is a chord and A...

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  14. In the given figure, a circle is inscribed in a quadrilateral ABCD tou...

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  15. In the given figure, DeltaABC is right-angled at B such that BC=6cm an...

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  16. In the given figure, PA and PB are tangents to the given circle such t...

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  17. In the given figure, DE and DF are tangents from and external point D ...

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  18. In the given figure, three circles with centres A, B, C respectively t...

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  19. In the given figure, AP, AQ and BC are tangents to the circle. If AB=5...

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  20. In the given figure, O is the centre of two concentric circles of radi...

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