Home
Class 9
MATHS
On the outside of the equilateral triang...

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.

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

In Delta ABC ,AD is a perpendicular drawn from A to the side BC. If AD^(2)=BD . CD , then prove that the triangle is a right-angled triangle.

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.

I is the incentre of the Delta ABC . The perpendicular drawn from I to BC intersects BC at. P. Prove that AB-AC=BP-CP .

The equilateral triangle ABC is inscribed in a circle. If P is any point on the ar BC, then prove that AB=PB+PC .

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)

OX,OY and OZ are the perpendiculars drawn from an internal point O of the Delta ABC on its sides BC,CA and AB respectively. Prove that AZ^(2) + BX^(2) + CY ^(2) = AY^(2) + CX^(2) + BZ^(2)

ABC is a right angled triangle , right angled at C and P is the length of perpendicular from C on AB. If a, b and C are the length of sides BC, CA and AB respectively. Then___

Circumradius of DeltaABC is 3 cm and its area is 6 cm^(2) . If DEF is the triangle formed by feet of the perpendicular drawn from A,B and C on the sides BC, CA and AB, respectively, then the perimeter of DeltaDEF (in cm) is _____

D, E and F are the mid-points of AB, BC and CA of the equilateral DeltaABC. Prove that DeltaDEF is also an equilateral triangle.

CALCUTTA BOOK HOUSE-THEOREMS ON AREAS-EXERCISE-3
  1. In the isosceles DeltaABC, AB = AC , O is any point on the side BC. OP...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. Prove that the sum of the perpendiculars drawn from any interior point...

    Text Solution

    |

  20. B is a vertex of the isosceles triangle ABC. D and E are the mid-point...

    Text Solution

    |