Home
Class 10
MATHS
In the given figure AB is the diameter o...

In the given figure AB is the diameter of a circle with centre O . If chord AC = chord AD, prove that :
(i) are ` BC= are DB `
(ii) AB is bisector of ` angle CAD .`
Further, if the length of are AC is twice the length of are BC , find :
(i) ` angle BAC `
(ii) ` angle ABC `

Text Solution

Verified by Experts

The correct Answer is:
` (a) angle BAC = 30 ^(@) (b) angle ABC = 60^(@) `
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    ICSE|Exercise EXERCISE 17(B) |10 Videos

  • CHAPTERWISE REVISION EXERCISE

    ICSE|Exercise CHAPTERWISE REVISION EXERCISE (PROBABILITY)|16 Videos

  • CONSTRUCTIONS (CIRCLES)

    ICSE|Exercise EXERCISE|39 Videos

Similar Questions

Explore conceptually related problems

In the given figure , find the length of chord AB .

In the given figure, O is the centre of the circle. If chord AB= chord AC, OP bot AB and OQ bot AC , show that: PB= QC

O is the centre of a circle of diameter AB. If chord AC= chord BC, then find the value of angleABC .

In the given figure, O is the centre of the circle and the length of arc AB is twice the length of arc BC. if angleAOB =100^(@) find angleBOC

In the figure AB is the chord of a circle with centre O and DOC is a line segment such that BC=DO . If /_C=20^(@) , find angle AOD.

In the given figure , the lengths of arc AB and are BC arc in the ratio 3: 2 if angle AOB = 96^(@) , find (i) angle CAB (ii) angle ADB

In the given figure , AD is a diameter O is the centre of the circle AD is parallel to BC and angle CBD = 32 ^(@) (i) angle OBD (ii ) angle AOB (iii) angle BED

In the figure, two equal chords AB and CD of a circle with centre O, intersect each other at E, Prove that AD=CB

In the figure, AD is perpendicular to BC, prove that AB+AC gt 2AD .

Find : (i) BC (ii) AD (iii) AC

ICSE-CIRCLES-EXERCISE 17( C )
  1. If I is the incentre of triangle ABC and AI when produced meets the c...

    Text Solution

    |

  2. In the given figure ,AB = AD = DC = PB and angle DBC = x^(@) Determ...

    Text Solution

    |

  3. In the given figure , ABC , AEQ and CEP are straight lines . Show that...

    Text Solution

    |

  4. In the given figure. AB is the diameter of the circle with centre O. ...

    Text Solution

    |

  5. In a cyclic -quadrilateral PQRS angle PQR = 135^(@) , Sides SP and...

    Text Solution

    |

  6. In the following figure , ABCD is a cyclic quadrilateral in which AD i...

    Text Solution

    |

  7. ABCD is a cyclic quadrilateral , Sides AB and DC produced meet at poin...

    Text Solution

    |

  8. The following figure shows a circle with PR as its diameter. If PQ= ...

    Text Solution

    |

  9. In the given figure AB is the diameter of a circle with centre O . If ...

    Text Solution

    |

  10. In cyclic quadrilateral ABCD , AD = BC , angle BAC = 30 ^(@) and angl...

    Text Solution

    |

  11. In cyclic quadrilateral ABCD , AD = BC , angle BAC = 30 ^(@) and angl...

    Text Solution

    |

  12. In cyclic quadrilateral ABCD , AD = BC , angle BAC = 30 ^(@) and an...

    Text Solution

    |

  13. In cyclic quadrilateral ABCD , AD = BC, angle BAC = 30 ^(@) and ang...

    Text Solution

    |

  14. In the given figure , angle ACE = 43^(@) and angle CAF = 62^(@) , fi...

    Text Solution

    |

  15. In the given figure,AB is parallel to DC. angle BCE = 80 ^(@) and an...

    Text Solution

    |

  16. ABCD is a cyclic quadrilateral of a circle with centre O such that AB ...

    Text Solution

    |

  17. In the figure , given below , CP bisects angle ACB. Show that DP bi...

    Text Solution

    |

  18. In cyclic quadrilateral ABCD , AD = BC , angle BAC = 30 ^(@) and angl...

    Text Solution

    |

  19. In the given figure , AD is a diameter O is the centre of the circle ...

    Text Solution

    |

  20. In the figure given , O is the centre of the circle . angle DAE = 70^...

    Text Solution

    |