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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,835

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: 88,882

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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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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: 15,605

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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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