Home
Class 10
MATHS
A B C is an isosceles triangle with A...

`A B C` is an isosceles triangle with `A C=B C` . If `A B^2=2\ A C^2` , prove that ` A B C` is right triangle.

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 a triangle A B C , if cos A+2\ cos B+cos C=2. prove that the sides of the triangle are in A.P.

In Figure, A B C is an isosceles triangle in which A B=A CdotC P A B and A P is the bisector of exterior /_C A D of A B C . Prove that /_P A C=/_B C A and (ii) A B C P is a parallelogram.

If A B C is an isosceles triangle such that A B=A C and A D is an altitude from A on B C . Prove that (i) /_B=/_C (ii) A D bisects B C (iii) A D bisects /_A

In triangle ABC if 2sin^(2)C=2+cos2A+cos2B , then prove that triangle is right angled.

In A B C , if r\ : r_1: R=2\ : 12\ :5, where all symbols have their usual meaning, then A B C is an acute angled triangle A B C is an obtuse angled triangle A B C is right angled which is not isosceles A B C is isosceles which is not right angled

If cos B=(sin A)/(2sin C) then prove that the triangle is isosceles.

In figure, ABC is a triangle in which /_A B C=90^@ and A D_|_B C . Prove that A C^2=A B^2+B C^2-2B C.B D .

ABC is a right isosceles triangle, right angled at B. Then sin^(2)A+cos^(2)C = _________

In figure, ABC is triangle in which /_A B C > 90o and A D_|_C B produced. Prove that A C^2=A B^2+B C^2+2B C.B D .

If in a Delta ABC, c(a+b) cos B//2 = b(a+c) cos C//2 , prove that the triangle is isosceles.

RD SHARMA-TRIANGLES-All Questions
  1. In a A B C ,\ \ A D|B C and A D^2=B DxxC Ddot Prove that A B C is a ...

    Text Solution

    |

  2. P and Q are points on the sides C A and C B respectively of A B C, ri...

    Text Solution

    |

  3. A B C is an isosceles triangle with A C=B C . If A B^2=2\ A C^2 , p...

    Text Solution

    |

  4. In P Q R ,\ \ Q M|P R and P R^2-P Q^2=Q R^2 . Prove that Q M^2=P M...

    Text Solution

    |

  5. Prove that the sum of the squares of the diagonals of parallelogram...

    Text Solution

    |

  6. If the sides of a triangle are 3 cm, 4 cm and 6 cm long, determine ...

    Text Solution

    |

  7. The sides of certain triangles are given below. Determine which of ...

    Text Solution

    |

  8. A man goes 15 metres due west and then 8 metres due north. How far ...

    Text Solution

    |

  9. A ladder 17m long reaches a window of a building 15m above the grou...

    Text Solution

    |

  10. Two poles of heights 6 m and 11 m stand on a plane ground. If the d...

    Text Solution

    |

  11. In an isosceles triangle A B C ,\ A B=A C=25 c m ,\ \ B C=14 c m . ...

    Text Solution

    |

  12. The foot of a ladder is 6m away from a wall and its top reaches a w...

    Text Solution

    |

  13. Two poles of height 9m and 14m stand on a plane ground. If the dist...

    Text Solution

    |

  14. Using Pythagoras theorem determine the length of A D in terms of ...

    Text Solution

    |

  15. A triangle has sides 5cm, 12cm and 13cm. Find the length to one dec...

    Text Solution

    |

  16. A B C D is a square. F is the mid-point of A Bdot B E is one ...

    Text Solution

    |

  17. In an isosceles triangle A B C , if A B=A C=13 cm and the altitu...

    Text Solution

    |

  18. In a A B C ,\ \ A B=B C=C A=2a and A D|B C . Prove that A D=asqrt(...

    Text Solution

    |

  19. The lengths of the diagonals of a rhombus are 24cm and 10cm. Find e...

    Text Solution

    |

  20. Each side of a rhombus is 10cm. If one of its diagonals is 16cm fin...

    Text Solution

    |