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The vertices of a triangle ABC are A(3, ...

The vertices of a triangle ABC are A(3, 0), B(0, 6) and C(6, 9). A line DE divides both AB and AC in the ratio 1 : 2 meeting AB in D and AC in E. Prove that `triangle ABC = 9 triangle ADE`.

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MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
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  2. If a ne b ne c, prove that (a, a^2), (b, b^2), (c, c^2) can never be c...

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  3. The vertices of a triangle ABC are A(3, 0), B(0, 6) and C(6, 9). A lin...

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  4. A and A’ be the points (5, 0) and (-5, 0) respectively. Find the equat...

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  5. The extremities of the base of an isosceles triangle are the points (2...

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  6. A line is such that its segment between the straight line 5x-y-4=0 and...

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  7. Find the distance of the line 4x - y = 0 from the point P (4, 1) measu...

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  8. Prove that the st. line ax + by + c = 0 divides the join of (x1, y1) a...

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  9. Prove that (-1, 4) is the orthocentre of the triangle formed by the li...

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  10. The equation of the perpendicular bisector of the side AB of a triangl...

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  11. Let the opposite angular points of a square be (3, 4) and (1, -1). Fin...

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  12. Using the concept of slope, prove that medians of an equilateral trian...

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  13. Show that the perpendicular drawn from the point (4, 1) on the line se...

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  14. A rectangle has opposite vertices at the points (1,2) and (5, 5). If t...

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  15. Find the centroid, incentre, circumcentre and orthocentre of the trian...

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  16. The vertices of a triangle are : P(x1,x1 tan theta1),Q (x2, x2tantheta...

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  17. The points (1, 3) and (5, 1) are the opposite vertices of a rectangle....

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  18. One side of a rectangle lies along the line 4x + 7y +5=0. Two of its v...

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  19. The consecutive sides of a parallelogram are 4x + 5y = 0 and 7x + 2y =...

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  20. One side of a square is inclined to the x-axis at an angle alpha and o...

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