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In the given figure, two circles touch e...

In the given figure, two circles touch each other at `C` and `AB` is a tangent to both the circles. The mesure of `/_ACB` is

A

`45^(@)`

B

`60^(@)`

C

`90^(@)`

D

`120^(@)`

Text Solution

Verified by Experts

Draw a tangent to the circles at point `C` . Let it meet `AB` at `P`.
Then, `PA=PC` and `PB=PC`
`PA=PCimplies/_PAC=/_PCA`
`PB=PCimplies/_PBC=/_PCB`
`:./_PAC+/_PBC=/_PCA+/_PCB=/_ACB`
`implies/_PAC+/_PBC+/_ACB=2/_ACB`
`implies180^(@)=2/_ACBimplies90^(@)`
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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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  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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