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## #1 2009-03-11 02:53:14

ganesh
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### 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 2013-03-25 06:21:58

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

Hi;

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

Last edited by bobbym (2013-03-25 07:00:48)

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
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## #3 2013-03-26 04:45:30

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

## #4 2013-03-26 04:53:17

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

Maybe it is supposed to be a sign for congruence?

The limit operator is just an excuse for doing something you know you can't.
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“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #5 2013-03-26 04:58:15

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

## #6 2013-04-05 19:49:06

hammana
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### 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

## #7 2013-04-05 22:56:52

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

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