Home
Class 10
MATHS
In triangle ABC, angle B = 90^@ and D is...

In `triangle ABC`, `angle B` = `90^@` and D is the mid point of BC. Prove that `AC^2` = `AD^2 + 3CD^2`.

Promotional Banner

Topper's Solved these Questions

  • STATISTICS AND PROBABILITY

    AGRAWAL PUBLICATION|Exercise EXAMPLE|124 Videos

Similar Questions

Explore conceptually related problems

In Delta ABC, angle B = 90^(@) and d is the mid - point of BC. Prove that AC ^(2) = AD^(2) + 3CD ^(2)

In a triangle ABC,B=90^(@) and D is the mid-oint of BC then prove that AC^(2)=AD^(2)+3CD^(2)

In the given figure ABC is a right angled triangle with angleB=90^(@) . D is the mid -point of BC . Show that AC^(2) = AD^(2) +3CD^(2) .

In right-angled triangle ABC in which /_C=90^(@), if D is the mid-point of BC, prove that AB^(2)=4AD^(2)-3AC^(2)

In Fig.3,ABC is a right triangle,right angled at C and D is the mid-point of BC.Prove that AB^(2)=4AD^(2)-3AC^(2)

In triangle ABC , angle ACB = 90^(@) , CD bot AB and DE bot CB Prove that CD^(2) xxAC = AD xx AB xxDE .

In a right ABC right-angled at C, if D is the mid-point of BC, prove that BC^(2)=4(AD^(2)-AC^(2))

In an isoscles Delta ABC, AB= AC and D is a point on BC. Prove that AB^(2)-AD^(2)=BD*CD .

In a triangle ABC,AC>AB,D is the mid- point of BC and AE perp BC .Prove that: (i) AC^(2)=AD^(2)+BCDE+(1)/(4)BC^(2)

AGRAWAL PUBLICATION-TRIANGLES-EXAMPLE
  1. Three 30^@ - 60^@ - 90^@ set squares are together as shown in the diag...

    Text Solution

    |

  2. In the figure, angle D = angle E and (AD)/(DB)=(AE)/(EC), prove that B...

    Text Solution

    |

  3. In triangle ABC, angle B = 90^@ and D is the mid point of BC. Prove th...

    Text Solution

    |

  4. Diagonals of a trapezium PQRS intersect each other at the point O, PQ|...

    Text Solution

    |

  5. In the figure, if AB||DC and AC, PQ intersect each other at the point ...

    Text Solution

    |

  6. In the given figure, if DE||BC, then find the ratio of ar(Delta ADE) a...

    Text Solution

    |

  7. ABCD is a trapezium in which AB||DC and P, Q are points on AD and BC r...

    Text Solution

    |

  8. Two right triangles ABC and DBC are drawn on the same hypotenuse BC an...

    Text Solution

    |

  9. Diagonals of a trapezium PQRS intersect each other at the point O, PQ|...

    Text Solution

    |

  10. In the given figure, if angle ACB = angle CDA, AC = 8 cm and AD = 3 cm...

    Text Solution

    |

  11. A 15 metres high tower coasts a shadow 24 metres long at a certain tim...

    Text Solution

    |

  12. If P and Q are the points on side CA and CB, respectively of triangle ...

    Text Solution

    |

  13. If the area of two similar triangles are equal, prove that they are co...

    Text Solution

    |

  14. There is a circular park of radius 24 m and there is a pole at a dista...

    Text Solution

    |

  15. There is a circular park of radius 24 m and there is a pole at a dista...

    Text Solution

    |

  16. D, E and F are respectively the mid points of the sides AB, AC and BC ...

    Text Solution

    |

  17. A flag pole 18 m high casts a shadow 9.6m long. Find the distance of t...

    Text Solution

    |

  18. If a line is drawn parallel to one side of a triangle to intersect oth...

    Text Solution

    |

  19. In the given figure, if PQRS is a parallelogram and AB||PS, then prove...

    Text Solution

    |

  20. triangle ABC figure, AD bot BC. Prove that AC^2 = AB^2 + BC^2 - 2BC xx...

    Text Solution

    |