Home
Class 9
MATHS
In the isosceles DeltaABC, AB = AC , O i...

In the isosceles `DeltaABC`, AB = AC , O is any point on the side BC. OP and OQ are the perpendicular distance of the sides AB and AC from O respectively. BD is the perpendicular distance of AC from B. Show that OP + OQ = BD.

Promotional Banner

Topper's Solved these Questions

  • THEOREMS ON AREAS

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-3|40 Videos

  • SET THEORY

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1|37 Videos

  • THEOREMS ON CONCURRENCE

    CALCUTTA BOOK HOUSE|Exercise EXERCISE Long-answer type questions|17 Videos

Similar Questions

Explore conceptually related problems

On the outside of the equilateral triangle ABC and in the angular region angleABC , O is a point. OP, OQ and OR are the perpendiculars drawn from O to the sides. AB, BC and CA respectively. Prove that the height of the triangle = OP + OQ - OR.

Triangle ABC is isosceles with AB=AC and BC=65cm. P is a point on BC such that the perpendiculardistances from P to AB and AC are 24cm and 36cm, respectively. The area of triangle ABC (in sq cm is)

AB and CD are two chords of a circle with centre at O , the ratio of lengths of which is 4: 5. If the perpendicular distance of AB from O be d cm, then perpendicular distance of CD from O.

In the isosceles triangle ABC, AB=AC and BE is perpendicular to AC from B. Prove that BC^(2) = 2ACxxCE

In a right triangle ABC right-angled at B, if P and Q are points on the side AB and AC respectively, then___

In the isosceles triangle ABC, AB=AC, if a circle is drawn with the side AB as diamter then the circle intersects the side BC at the point D. When BD=4 cm , find the the length of CD.

D is the mid-point of BC of DeltaABC . E and O are the mid-points of BD and AE respectively. Then the area of the triangle BOE is-

ABC is an isosceles triangle in which altitudes BD and CE are drawn to equal sides AC and AB respectively (see figure) Show that these altitudes are equal.

In the figure D, E are points on the sides AB and AC respectively of DeltaABC such that ar(DeltaDBC) = ar(DeltaEBC) . Prove that DE || BC.

CALCUTTA BOOK HOUSE-THEOREMS ON AREAS-EXERCISE-3
  1. The area of the parallelogram ABCD is 44 sq.cm. P is the mid-point of ...

    Text Solution

    |

  2. A square and a rhombus stand on the same base of length 10 cms. Show t...

    Text Solution

    |

  3. In the isosceles DeltaABC, AB = AC , O is any point on the side BC. OP...

    Text Solution

    |

  4. In the trapezium ABCD, AB || DC. The diagonals AC and BD of it interse...

    Text Solution

    |

  5. Prove that the line segment joining the mid-points of the lateral side...

    Text Solution

    |

  6. Side of a equilateral triangle is 7 ,find its hight.

    Text Solution

    |

  7. If a square and a rhombus lie on the same base, then find logically wh...

    Text Solution

    |

  8. Prove that the area of a rhombus is half the area of the rectangle pro...

    Text Solution

    |

  9. D, E and F are the mid-points of the sides AB, BC and CA of the DeltaA...

    Text Solution

    |

  10. If E be the mid-point of the median AD of DeltaABC, then prove that De...

    Text Solution

    |

  11. Prove that two diagonals of a parallelogram divides it into four trian...

    Text Solution

    |

  12. P is any point on AD, the median of DeltaABC. Prove that DeltaABP=Delt...

    Text Solution

    |

  13. P is any point in the interior of the parallelogram ABCD. Prove that D...

    Text Solution

    |

  14. In the trapezium ABCD, AB || DC and the diagonals AC and BD intersects...

    Text Solution

    |

  15. The diagonals AC and BD of a quadrilateral ABCD intersects each other ...

    Text Solution

    |

  16. D and E lie on the side AB and AC of DeltaABC such that DeltaDBC=Delta...

    Text Solution

    |

  17. Prove that if each diagonal of a quadrilateral bisects it into two tri...

    Text Solution

    |

  18. Find the co ordinate on the X axis cut by the straight line 2x+3y=12

    Text Solution

    |

  19. On the outside of the equilateral triangle ABC and in the angular regi...

    Text Solution

    |

  20. D is the mid-point of the side BC of the DeltaABC and P is any point o...

    Text Solution

    |