Home
Class 12
MATHS
A circle is drawn in a sector of a large...

A circle is drawn in a sector of a larger circle of radius `r ,` as shown in figure. The smaller circle is tangent to the two bounding radii and the arc of the sector. The radius of the smaller circle is `r/2` (b) `r/3` (c) `(2sqrt(3)r)/5` (d) `r/(sqrt(2))`

A

`r/2`

B

`r/3`

C

`(2sqrt3r)/5`

D

`r/sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the radius of smaller circle be x. Here,
`OP=xcosec30^@`
`andOQ=r=xcosec30^@`
`rArr =x=r/3`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|17 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.14|1 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|2 Videos

Similar Questions

Explore conceptually related problems

A circle is drawn in a sector of a larger circle of radius r, as shown in the adjacent figure. The smaller circle is tangent to the two bounding radii and the are of the sector. The radius of the small circle is-

A B C D is a square of unit area. A circle is tangent to two sides of A B C D and passes through exactly one of its vertices. The radius of the circle is (a) 2-sqrt(2) (b) sqrt(2)-1 (c) sqrt(2)-1/2 (d) 1/(sqrt(2))

If the radius of the circle is r then find the area of circle?

A circle of radius 2 has its centre at (2, 0) and another circle of radius 1 has its centre at (5, 0). A line is tangent to the two circles at point in the first quadrant. The y-intercept of the tangent line is

In the given figure, what is the radius of the inscribed circle? 3/2 (b) 5/2 (c) 7/5 (d) none of these

If two concentric circles are of radii 5 cm and 3 cm, then the length of the chord of the larger circle which touches the smaller circle is___

ABCD be a cyclic quadrilateral inscribed in a circle of radius R. In previous problem the radius of the latter circle is

The locus of the mid-points of the chords of the circle of lines radiùs r which subtend an angle pi/4 at any point on the circumference of the circle is a concentric circle with radius equal to (a) (r)/(2) (b) (2r)/(3) (c) (r )/(sqrt(2)) (d) (r )/(sqrt(3))

Find the rate of change of the area of a circle with respect to its radius r when r=7cm .

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -Exercises
  1. (1-tanalphatanbeta)^2+(tanalpha+tanbeta)^2=

    Text Solution

    |

  2. Let A0A1A2A3A4A5 be a regular hexagon inscribed in a circle of unit ra...

    Text Solution

    |

  3. A circle is drawn in a sector of a larger circle of radius r , as show...

    Text Solution

    |

  4. A right triangle has perimeter of length 7 and hypotenuse of length 3....

    Text Solution

    |

  5. Given that the side length of a rhombus is the geometric mean of the ...

    Text Solution

    |

  6. Which of the following is correct?

    Text Solution

    |

  7. The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

    Text Solution

    |

  8. If sin^2theta=(x^2+y^2=1)/(2x) , then x must be -3 (b) -2 (c) 1 (d)...

    Text Solution

    |

  9. sec^2theta=4xy/(x+y)^2 is true if and only if

    Text Solution

    |

  10. If sinx+siny+sinz=3," then "cosx+cosy+cosz is equal to

    Text Solution

    |

  11. If sinx+sin y+sinz+sinw=-4, then the value of sin^(400)x+sin^(300)y+si...

    Text Solution

    |

  12. Prove that, SinA/(1-cosA) =CosecA+cotA

    Text Solution

    |

  13. If 1+sinx+sin^2x+sin^3x+oo is equal to 4+2sqrt(3),0<x<pi, then x is eq...

    Text Solution

    |

  14. The value of expression (2sin^2 91^0-1)(2sin^2 92^0-1)......(2sin^2 18...

    Text Solution

    |

  15. If sinA=sin^2Ba n d2cos^2A=3cos^2B then the triangle A B C is right an...

    Text Solution

    |

  16. If sintheta+costheta=1/5and 0lethetaltpi" then "cottheta is

    Text Solution

    |

  17. If π<α<(3π)/2 then sqrt((1-cosalpha)/(1+cosalpha))+sqrt((1+cosalpha)/...

    Text Solution

    |

  18. If 0 < alpha < pi/ 6 then alpha(cosec alpha) is

    Text Solution

    |

  19. The least value of 3sin^2theta+4cos^2theta is

    Text Solution

    |

  20. The minimum value of sin^4theta+cos^4theta is

    Text Solution

    |