Home
Class 12
MATHS
One vertex of a triangle of given specie...

One vertex of a triangle of given species is fixed and another moves along circumference of a fixed circle. Prove that the locus of the remaining vertex is a circle and find its radius.

Text Solution

Verified by Experts

The correct Answer is:
`(sinbeta)/(singamma)`
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    ARIHANT MATHS|Exercise EXAMPLE|2 Videos

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise For Session 1|18 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos

Similar Questions

Explore conceptually related problems

If on a given base B C , a triangle is described such that the sum of the tangents of the base angles is m , then prove that the locus of the opposite vertex A is a parabola.

If a circle of constant radius 3k passes through the origin and meets the axes at Aa n dB , prove that the locus of the centroid of triangle OA B is a circle of radius 2cdot

The base AB of a triangle is fixed and its vertex C moves such that sin A =k sin B (kne1) . Show that the locus of C is a circle whose centre lies on the line AB and whose radius is equal to (ak)/((1-k^2)) , a being the length of the base AB.

A parabola, of latus-rectum l, touch a fixed equal parabola, the axes of two parabola, being parallel. Prove that the locus of the vertex of the moving parabola is a parabola of latus rectum 2l.

Area of an equilateral triangle is 17300 cm^2 . By taking each vertex of the triangle as centre, a circle is drawn at each vertex. The radius of thecircleis half of the length of the side of an equilateral triangle. Find the area of that portion of the triangle which is not included in the circle. (pi=3.14 and sqrt3=1.73 )

The radius of the circle is 14 m. Find the radius of another circle whose area is one. fourth of the area of pervious circle.

Prove that the equation x^2 + y^2 + 2gx + 2fy + c = 0 represents a circle and find its centre and radius.

A body moves on a circular path of radius 1 m. It completes one circle in 2 seconds. Find its speed.

The area of an equilateral triangle ABC is 17320.5 cm^2 . With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see Fig. 12.28). Find the area of the shaded region. (Use pi=3.14 and sqrt3=1.73205 )

The area of an equilateral triangle ABC is 17320.5 cm^(2) . With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle. Find the area of the shaded region. (Use pi=3.14 and sqrt(3)=1.73205 )

ARIHANT MATHS-CIRCLE -Exercise (Questions Asked In Previous 13 Years Exam)
  1. One vertex of a triangle of given species is fixed and another moves a...

    Text Solution

    |

  2. Find the derivative of (a/x^4 - b/x^2 + cosx)

    Text Solution

    |

  3. If the circles x^2+y^2+2a x+c y+a=0 and points Pa n dQ , then find the...

    Text Solution

    |

  4. A circle touches the x-axis and also touches the circle with center (0...

    Text Solution

    |

  5. Find the derivative of (4x - 2)

    Text Solution

    |

  6. Let ABCD be a square of side length 2 units. C2 is the circle through ...

    Text Solution

    |

  7. ABCD is a square of side length 2 units. C(1) is the circle touching ...

    Text Solution

    |

  8. ABCD is a square of side length 2 units. C(1) is the circle touching ...

    Text Solution

    |

  9. If the lines 3x-4y-7=0 and 2x-3y-5=0 are two diameters of a circle of ...

    Text Solution

    |

  10. Let C be the circle with centre (0, 0) and radius 3 units. The equatio...

    Text Solution

    |

  11. Find the derivative of (ax + b)^n

    Text Solution

    |

  12. Consider a family of circles which are passing through the point (-1,1...

    Text Solution

    |

  13. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

    Text Solution

    |

  14. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

    Text Solution

    |

  15. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

    Text Solution

    |

  16. Consider: L1:2x+3y+p-3=0 L2:2x+3y+p+3=0 where p is a real number and...

    Text Solution

    |

  17. The point diametrically opposite to the point P(1, 0) on the circle x^...

    Text Solution

    |