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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 17,001

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,974

Hi;

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

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

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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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,922

Maybe it is supposed to be a sign for congruence?

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**hammana****Member**- Registered: 2012-03-02
- Posts: 48

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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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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