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#1 2009-03-10 03:53:14

ganesh
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Registered: 2005-06-28
Posts: 14,522

Question Bank : Age Group 14-15 : XI

1. Find the equation of the straight line joining the point of intersection of 3x - y + 9 = 0 and
2y + x - 4 = 0 to the point of intersection of 2x + y = 4 and 2y = x + 3.

2. The vertices of a triangle ABC are A (-3, 3), B (-1, -4), and C (5, -2). M and N are the midpoints of AB and AC. Show that MN is parallel to BC and

.

3. Find the equation of the line parallel to the Y axis and passing through the point of intersection of 3x - 4y - 9 = 0 and x - 4y - 2 = 0.

4. Find the orthocenter of the triangle whose vertices are (-2, 1), (-1, -4), and (0, -5).

5. Prove that the line segments joining the mid points of the adjacent sides of a rhombus form a rectangle.

6. ABCD is a trapezium with AB || CD. The diagonals AC and BD intersect at E. If
Δ AED ||| Δ BEC, prove that AD = BC.

7. Two circles intersect each other internally at P. If ACP and BDP are the lines meeting the two circles at A, B and C, D respectively, prove that

.

8. Show that

.

9. If A = 30°, and B = 60°, verify that
(i) sin(A + B) = sin A cos B + cos A sin B
(ii) cos(A + B) = cos A cos B - sinA sin B.

10. From the top of a building 60 meters high, the angle of depression of the top and bottom of a tower are observed to be 30° and 60° respectively. Find the height of the tower.


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#2 2013-03-24 07:21:58

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,200

Re: Question Bank : Age Group 14-15 : XI

Hi;

4) The orthocenter is located at (-10,-7).

Last edited by bobbym (2013-03-24 08:00:48)


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2013-03-25 05:45:30

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,142
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Re: Question Bank : Age Group 14-15 : XI

What is the meaning of |||?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
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#4 2013-03-25 05:53:17

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Question Bank : Age Group 14-15 : XI

Maybe it is supposed to be a sign for congruence? dunno


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#5 2013-03-25 05:58:15

Agnishom
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From: The Complex Plane
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Posts: 17,142
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Re: Question Bank : Age Group 14-15 : XI

Then question 6 would be not a question at all.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You made a human being happy! There is no further achievement.' -bobbym

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#6 2013-04-04 20:49:06

hammana
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Registered: 2012-03-02
Posts: 48

Re: Question Bank : Age Group 14-15 : XI

Hi Agnishom

Question 6 means probably that triangles AED and BEC are similar . We have to proof that: 

if EB/EA=EC/ED, then AD=BC.

EB/EA=EC/ED -->EB*ED=EA*EC --> A,B,C,D are concyclic --> AD=BC

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#7 2013-04-04 23:56:52

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,142
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Re: Question Bank : Age Group 14-15 : XI

1. How does that make them concyclic?
2. How can you say that the opposite sides of a concyclic quadrilateral are equal?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You made a human being happy! There is no further achievement.' -bobbym

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