Home
Class 12
MATHS
Three parallel chords of a circle have l...

Three parallel chords of a circle have lengths 2,3,4 units and subtend angles `alpha,beta,alpha+beta` at the centre, respectively `(alpha

Text Solution

Verified by Experts

From the given information we have the following diagram.
`AB = 4, AC = 2, BC = 3`
Using the geometry of the circle, we have `angle ABC = alpha//2`
Now in `Delta ABC`, using cosine rule

`cos (alpha//2) = ((3)^(2) + (4)^(2) - (2)^(2))/(2 xx (3) xx (4)) = (7)/(8)`
`rArr cos alpha = 2 cos^(2) (alpha//2) -1`
`= 2 xx (49)/(64) - 1 = (17)/(31)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Concept application exercise 5.1|12 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Concept application exercise 5.2|8 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Archives (Numerical Value Type)|3 Videos

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise Archives(Matrix Match Type)|1 Videos

Similar Questions

Explore conceptually related problems

Factorise alpha^2 +beta^2 + alpha beta

Let alpha chord of a circle be that chord of the circle which subtends an angle alpha at the center. If the slope of a pi//3 chord of x^(2)+y^(2)=4 is 1, then its equation is

alpha + beta = 5 , alpha beta= 6 .find alpha - beta

Let alpha chord of a circle be that chord of the circle which subtends an angle alpha at the center. The distance of 2pi //3 chord of x^(2)+y^(2)+2x+4y+1=0 from the center is

Let alpha chord of a circle be that chord of the circle which subtends an angle alpha at the center. If x+y=1 is a chord of x^(2)+y^(2)=1 , then alpha is equal to

If alpha and beta are zeroes of the polynomial 3x^(2)+6x+1 , then find the value of alpha+beta+alpha beta .

The lengths of the sides of a triangle are alpha-beta, alpha+beta and sqrt(3alpha^2+beta^2), (alpha>beta>0) . Its largest angle is

Find the condition that the chord of contact of tangents from the point (alpha, beta) to the circle x^2 + y^2 = a^2 should subtend a right angle at the centre. Hence find the locus of (alpha, beta) .

Find the condition that the chord of contact of tangents from the point (alpha, beta) to the circle x^2 + y^2 = a^2 should subtend a right angle at the centre. Hence find the locus of (alpha, beta) .

If the eccentric angles of the extremities of a focal chord of an ellipse x^2/a^2 + y^2/b^2 = 1 are alpha and beta , then (A) e = (cos alpha + cos beta)/(cos (alpha + beta)) (B) e= (sin alpha + sin beta)/(sin(alpha + beta)) (C) cos((alpha-beta)/(2)) = e cos ((alpha + beta)/(2)) (D) tan alpha/2.tan beta/2 = (e-1)/(e+1)

CENGAGE ENGLISH-PROPERTIES AND SOLUTIONS OF TRIANGLE-Illustration
  1. In a triangle, if the angles A , B ,a n dC are in A.P. show that 2cos1...

    Text Solution

    |

  2. If a=9,b=4a n dc=8 then find the distance between the middle point of ...

    Text Solution

    |

  3. Three parallel chords of a circle have lengths 2,3,4 units and subtend...

    Text Solution

    |

  4. In a cyclic quadrilateral PQRS, PQ= 2 units, QR= 5 units, RS=3 units ...

    Text Solution

    |

  5. For any triangle ABC, prove that a(bcosC-ccosB)=b^2-c^2

    Text Solution

    |

  6. If in a triangle a cos^2C/2+cos^2A/2=(3b)/2, then find the relation be...

    Text Solution

    |

  7. Prove that (b+c)cosA+(c+a)cosB+(a+b)cosC=2sdot

    Text Solution

    |

  8. If cosA/2=sqrt((b+c)/(2c)) , then prove that a^2+b^2=c^2dot

    Text Solution

    |

  9. If the cotangents of half the angles of a triangle are in A.P., then ...

    Text Solution

    |

  10. If the sides a , ba n dCof A B C are in AdotPdot, prove that 2sinA/2s...

    Text Solution

    |

  11. Prove that (cotA/2+cotB/2)(asin^2B/2+bsin^2A/2)=ccotC/2

    Text Solution

    |

  12. Find the value of tan A, if area of Delta ABC is a^(2) -(b-c)^(2).

    Text Solution

    |

  13. Prove that a^(2) sin 2B + b^(2) sin 2A = 4 Delta

    Text Solution

    |

  14. Prove that ((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^2c^2)=sin^2A

    Text Solution

    |

  15. If the sides of a triangle are 17 , 25a n d28 , then find the greatest...

    Text Solution

    |

  16. In equilateral triangle ABC with interior point D, if the perpendicula...

    Text Solution

    |

  17. If area of a triangle is 2 sq. units, then find the value of the pr...

    Text Solution

    |

  18. A triangle has sides 6,7, and 8. The line through its incenter para...

    Text Solution

    |

  19. Each side of triangle ABC is divided into three equal parts. Find the ...

    Text Solution

    |

  20. The two adjacent sides of a cyclic quadrilateral are 2a n d5 and the a...

    Text Solution

    |