Home
Class 10
MATHS
In a triangle PQR, L and M are two point...

In a triangle PQR, L and M are two points on the base QR, such that `angleLPQ = angleQRP` and `angleRPM = angleRQP.` Prove that:
`QL xxRM = PL xx PM`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • MIXED PRACTICE

    ICSE|Exercise SET B|52 Videos
  • MEASURES OF CENTRAL TENDENCY (MEAN, MEDIAN, QUARTILES AND MODE)

    ICSE|Exercise EXERCISE 24 (E)|23 Videos
  • PROBABILITY

    ICSE|Exercise EXERCISE 25(C)|106 Videos

Similar Questions

Explore conceptually related problems

In a triangle PQR, L and M are two points on the base QR, such that angleLPQ = angleQRP and angleRPM = angleRQP. Prove that: PQ^2=QR xxQL

In a triangle PQR, L and M are two points on the base QR, such that angleLPQ = angleQRP and angleRPM = angleRQP. Prove that: DeltaPQL ~ DeltaRPM

In a triangle PQR, L and M are two points on the base QR, such that /_LPQ = /_QRP and /_RPM = /_RQP . Prove that: QL xx RM = PL xx PM

In a triangle PQR, L and M are two points on the base QR, such that /_LPQ = /_QRP and /_RPM = /_RQP . Prove that: PQ^2 = QR xx QL

In a triangle PQR, L and M are two points on the base QR, such that /_LPQ = /_QRP and /_RPM = /_RQP . Prove that: DeltaPQL ~ Delta RPM

The sides PQ, PR of triangle PQR are equal, and S, T are points on PR, PQ such that angle PSQ and anglePTR are right angles If OS and RT intersect at M, prove that the triangles PTM and PSM are congruent.

In triangle P Q R , if P Q=R Q\ a n d\ L ,\ M\ a n d\ N are the mid-points of the sides P Q ,\ Q R\ a n d\ R P respectively. Prove that L N=M N .

In a triangle \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B C . Prove that: a r\ (triangle \ L O B)=a r\ (triangle \ M O C)

In triangle ABC, the medians BP and CQ are produced upto points M and N respectively such that BP = PM and CQ = QN. Prove that: M, A and N are collinear.

In Delta P Q R , if P Q=Q R and L ,M and N are the mid-points of the sides P Q ,Q R and R P respectively. Prove that L N=M Ndot

ICSE-MIXED PRACTICE -SET B
  1. The line 3x - 4y + 12 = 0 meets x-axis at point A and y-axis at point ...

    Text Solution

    |

  2. In a triangle PQR, L and M are two points on the base QR, such that an...

    Text Solution

    |

  3. In a triangle PQR, L and M are two points on the base QR, such that an...

    Text Solution

    |

  4. In a triangle PQR, L and M are two points on the base QR, such that an...

    Text Solution

    |

  5. In a rectangle ABCD, its diagonal AC = 15 cm and angleACD = alpha If ...

    Text Solution

    |

  6. The given figure shows, AB is a diameter of the circle. Chords AC and ...

    Text Solution

    |

  7. Use ruler and compasses for this question. Construct an isosceles tr...

    Text Solution

    |

  8. Use ruler and compasses for this question. Draw AD, the perpendicula...

    Text Solution

    |

  9. Use ruler and compasses for this question. Draw a circle with centre...

    Text Solution

    |

  10. In triangle ABC, angleBAC = 90^@, AB = 6 cm and BC = 10 cm. A circle ...

    Text Solution

    |

  11. A conical vessel of radius 6 cm and height 8 cm is completely filled w...

    Text Solution

    |

  12. Prove that : (1+cotA)/(cosA)+(1+tanA)/(sinA)=2(secA+"cosec"A)

    Text Solution

    |

  13. Prove that : sqrt((1+sinA)/(1-sinA))-sqrt((1-sinA)/(1+sinA))=2tanA

    Text Solution

    |

  14. Solve for 0^@ le x le 90^@ 3 tan^(2)(2x-20^@)=1

    Text Solution

    |

  15. Solve for x in W, 0^@ le x le 90^@ tan^2x=3(secx-1)

    Text Solution

    |

  16. The angle of elevation of the top of a tower as observed from a point ...

    Text Solution

    |

  17. The mean of the following frequency distribution is 50, but the freque...

    Text Solution

    |

  18. A card is drawn at random from a well-shuffled deck of 52 playing card...

    Text Solution

    |

  19. A card is drawn at random from a well-shuffled deck of 52 playing card...

    Text Solution

    |

  20. A card is drawn at random from a well-shuffled deck of 52 playing card...

    Text Solution

    |