Home
Class 11
MATHS
A B C is a right-angled triangle in whic...

`A B C` is a right-angled triangle in which `/_B=90^0` and `B C=adot` If `n` points `L_1, L_2, ,L_nonA B` is divided in `n+1` equal parts and `L_1M_1, L_2M_2, ,L_n M_n` are line segments parallel to `B Ca n dM_1, M_2, ,M_n` are on `A C ,` then the sum of the lengths of `L_1M_1, L_2M_2, ,L_n M_n` is `(a(n+1))/2` b. `(a(n-1))/2` c. `(a n)/2` d. none of these

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

ABC is a right-angled triangle in which angleB=90^(@) and BC=a. If n points L_(1),L_(2),…,L_(n) on AB is divided in n+1 equal parts and L_(1)M_(1), L_(2)M_(2),…,L_(n)M_(n) are line segments paralllel to BC and M_(1), M_(2),….,M_(n) are on AC, then the sum of the lengths of L_(1)M_(1), L_(2)M_(2),...,L_(n)M_(n) is

If l ,\ m,\n are three lines such that l || m\ a n d\ n_|_l , prove that n_|_mdot

ABCD is a square of length a, a in N , a > 1. Let L_1, L_2 , L_3... be points on BC such that BL_1 = L_1 L_2 = L_2 L_3 = .... 1 and M_1,M_2 , M_3,.... be points on CD such that CM_1 = M_1M_2= M_2 M_3=... = 1 . Then sum_(n = 1)^(a-1) ((AL_n)^2 + (L_n M_n)^2) is equal to :

The direction cosines of a line satisfy the relations lambda(l+m)=na n dm n+n l+l m=0. The value of lambda, for which the two lines are perpendicular to each other, is a. 1 b. 2 c. 1//2 d. none of these

The direction cosines of the lines bisecting the angle between the line whose direction cosines are l_1, m_1, n_1 and l_2, m_2, n_2 and the angle between these lines is theta , are

A B C D is a parallelogram. L\ a n d\ M are points on A B\ a n d\ D C respectively and A L=C M . Prove that L M\ a n d\ B D bisect each other.

In A B C , let L ,M ,N be the feet of the altitudes. The prove that sin(/_M L N)+sin(/_L M N)+sin(/_M N L)=4sinAsinBsinC

In Fig. 4.237, L M=L N=46o . Express x in terms of a ,\ b and c where a ,\ b ,\ c are lengths of L M ,\ M N and N K respectively. (FIGURE)

Diagonals of a parallelogram A B C D intersect at O. dotA L\ a n d\ C M are perpendiculars to B D such that L\ a n d\ M lie on B D . IS A L=C M ? why or why not?

In a triangle A B C ,\ B M\ a n d\ C N are perpendiculars from B\ a n d\ C respectively on any line passing through A . If L is the mid-point of B C , prove that M L=N L . .

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If a,b,c,d be in G.P. show that (b-c)^2+(c-a)^2+(d-b)^2=(a-d)^2.

    Text Solution

    |

  2. If the pth, qth, rth, and sth terms of an A.P. are in G.P., then p-q ,...

    Text Solution

    |

  3. A B C is a right-angled triangle in which /B=90^0 and B C=adot If n po...

    Text Solution

    |

  4. If (1-p)(1+3x+9x^2+27 x^3+81 x^4+243 x^5)=1-p^6,p!=1 , then the value ...

    Text Solution

    |

  5. ABCD is a square of length a, a in N, a > 1. Let L1, L2 , L3... be poi...

    Text Solution

    |

  6. Let Tr a n dSr be the rth term and sum up to rth term of a series, res...

    Text Solution

    |

  7. If (1+3+5++p)+(1+3+5++q)=(1+3+5++r) where each set of parentheses cont...

    Text Solution

    |

  8. If a x^3+b x^2+c x+d is divisible by a x^2+c ,t h e na ,b ,c ,d are in...

    Text Solution

    |

  9. The line x+ y = 1 meets X-axis at A and Y-axis at B,P is the mid-poin...

    Text Solution

    |

  10. In a geometric series, the first term is a and common ratio is rdot If...

    Text Solution

    |

  11. If x ,y ,a n dz are distinct prime numbers, then (a).x , y , a n dz ma...

    Text Solution

    |

  12. If x ,y , and z are in G.P. and x+3,y+3, and z+3 are in H.P., then y=2...

    Text Solution

    |

  13. If A.M., G.M., and H.M. of the first and last terms of the series of 1...

    Text Solution

    |

  14. The sum 1+3+7+15+31+...to100 terms is a. 2^(100)-102 b. 2^(99)-101 c...

    Text Solution

    |

  15. In a sequence of (4n + 1) terms the first (2n + 1) terms are in AP wh...

    Text Solution

    |

  16. The coefficient of x^(49) in the product (x-1)(x-3)(x-99)i s a. -99^...

    Text Solution

    |

  17. Let S=4/(19)+(44)/(19^2)+(444)/(19^3)+ u ptooo . Then s is equal to a....

    Text Solution

    |

  18. If Hn=1+1/2+...+1/ndot , then the value of Sn=1+3/2+5/3+...+(99)/(50) ...

    Text Solution

    |

  19. If the sum to infinity of the series 1+2r+3r^2+4r^3+ is 9/4, then val...

    Text Solution

    |

  20. The sum o f series 1+4/5+7/(5^2)+(10)/(5^3)+oo is a. 7//16 b. 5//16 ...

    Text Solution

    |