Home
Class 10
MATHS
In figure, P is the mid-point of B C , ...

In figure, `P` is the mid-point of `B C , ,Q` is the mid-point of `A P` , such that `B Q` produced meets `A C` at `Rdot` Prove that `3RA= CA`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • SURFACE AREAS AND VOLUMES

    RD SHARMA|Exercise All Questions|417 Videos
  • TRIGONOMETRIC IDENTITIES

    RD SHARMA|Exercise All Questions|254 Videos

Similar Questions

Explore conceptually related problems

In Figure, A B C D is a parallelogram in which P is the mid-point of D C and Q is a point on A C such that C Q=1/4A Cdot If P Q produced meets B C at Rdot Prove that R is a mid-point of B Cdot

In Figure, A B C D is a parallelogram in which P is the mid-point of D C\ a n d\ Q is a point on A C such that C Q=1/4A Cdot If P Q produced meets B C\ a t\ R , prove that R is a mid-point of B C

In the figure,M is the mid point of CA.DM produced meet BA at B N also AN=AM Prove that (BD)/(BN)=(DC)/(CM) .

D is the mid-point of side B C of A B C and E is the mid-point of B Ddot If O is the mid-point of A E , prove that a r( B O E)=1/8a r( A B C)

In A A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A Pdot Prove that: a r\ ( P B Q)=\ a r\ (\ A R C)

In A A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A Pdot Prove that: a r\ ( R Q C)=3/8\ a r\ (\ A B C)

In A A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A Pdot Prove that: a r\ (\ P R Q)=1/2a r\ (\ A R C)

In a A B C ,\ E\ a n d\ F are the mid-points of A C\ a n d\ A B respectively. The altitude A P\ to\ B C intersects F E\ at Qdot Prove that A Q=Q P

P is the mid-point of side AB of a parallelogram ABCD .A Line through B parallel to PD meets DC at Q and AD produced at R. Prove that ( i )AR=2BC (ii) BR=2BQ.

P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, show that (i) a r" "(P R Q)""=1/2a r""(A R C) (ii) a r" "(R Q C)""=3/8a r" "(A B C) (iii) a r" "(P B Q)" "=""a r" "(ARC)

RD SHARMA-TRIANGLES-All Questions
  1. In Figure, /B A C=90^0,A D is its bisector. If D E|A c , prove that D...

    Text Solution

    |

  2. Prove that the line segments joints joining the mid-points of the a...

    Text Solution

    |

  3. In figure, P is the mid-point of B C , ,Q is the mid-point of A P ,...

    Text Solution

    |

  4. A vertical stick 12m long casts a shadow 8m long on the ground. At the...

    Text Solution

    |

  5. In a quadrilateral A B C D , if bisectors of the /A B Ca n d/A D C mee...

    Text Solution

    |

  6. In A B C , the bisector of /B meets A C at Ddot A line P Q A C meets...

    Text Solution

    |

  7. The bisectors of the angles B and C of a triangle A B C , meet the o...

    Text Solution

    |

  8. In A B C ,/B=2/C and the bisector of /B intersects A C at Ddot Prove ...

    Text Solution

    |

  9. In Figure, D E B C , if A D=x ,D B=x-2,A E=x+2 and E C=x-1, find the ...

    Text Solution

    |

  10. Lex X by any point on the side BC of a triangle ABC. If XM, XN are d...

    Text Solution

    |

  11. In Figure P Q is parallel to M Ndot if (K P)/(P M)=4//13 and K N=20. 4...

    Text Solution

    |

  12. In Figure D E B C and C D E Fdot Prove that A D^2=A BxA Fdot

    Text Solution

    |

  13. Da n dE are respectively the points on the side A Ba n dA C of a A B ...

    Text Solution

    |

  14. ABCD is a parallelogram. P is a point on the side BC DP when produced ...

    Text Solution

    |

  15. In Figure D E A C and D C a pdot Prove that (B E)/(E C)=(B C)/(C P)

    Text Solution

    |

  16. Prove that the area of equilateral triangle described on the side of a...

    Text Solution

    |

  17. Equilateral triangles are drawn on the sides of a right triangle. Show...

    Text Solution

    |

  18. Two triangle ABC and D B C lie on the same side of the base B C . From...

    Text Solution

    |

  19. A B C D is a quadrilateral; P , Q , Ra n dS are the points of trisecti...

    Text Solution

    |

  20. A B C D is a parallelogram and A P Q is a straight line meeting B C at...

    Text Solution

    |