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If O, H and G represents circum centre, ...

If O, H and G represents circum centre, orthocentre and centroid respectively, then show
`HG:GO=2:1.` We have,

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`HG:GO=2:1`
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Let O, O' and G be the circumcentre, orthocentre and centroid of a Delta ABC and S be any point in the plane of the triangle. Statement -1: vec(O'A) + vec(O'B) + vec(O'C)=2vec(O'O) Statement -2: vec(SA) + vec(SB) + vec(SC) = 3 vec(SG)

If coordinates of the circum centre and the orthocentre of a triangle respectively (5,5) and (2,2) then the coordinates of the centroid are

ABC is a triangle whose circumcentre, incentre and orthocentre are O, I and H respectively which lie inside the triangle, then :

O,G,I and H are respectively the circumcentre, centroid, incentre and orthocentre of an equilateral triangle. Which of these points are identical ? / O, G, I तथा H क्रमशः एक समबाह त्रिभुज के परिकेंद्र, केंद्रक, अंतःकेंद्र और लम्बकेंद्र हैं | निम्न में से कौन से बिंदु समसरूप हैं ?

O, G, I and H are respectively the circumcenter, centroid, incentre and orthocentre of an equilateral triangle. which of these points are identical? किसी समबाहु त्रिभज में O, G, I और H क्रमशः परिकेद्र(circumcentre), केंद्रिका (centroid),अंत:केंद्र(incentre)और लंबकेंद्र (orthocentre) है| इनमें से कौन से बिंदु एक समान हैं?

If O is the circumcentre,G is the centroid and O' is orthocentre or triangle ABC then prove that: vec OA+vec OB+vec OC=vec OO

Assertion (A): If (-1,3,2) and (5,3,2) are respectively the orthocentre and circumcentre of a triangle, then (3,3,2) is its centroid. Reason (R): Centroid of a triangle divides the line segment joining the orthocentre and the circumcentre in the ratio 1:2 ,

Statement 1: If in a triangle, orthocentre, circumcentre and centroid are rational points, then its vertices must also be rational points. Statement : 2 If the vertices of a triangle are rational points, then the centroid, circumcentre and orthocentre are also rational points.

ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If O, H and G represents circum centre, orthocentre and centroid respe...

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  2. In a triangle XYZ, let x, y, z be the lengths of sides opposite to the...

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  3. In a triangle the sum of two sides is x and the product of the same is...

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  4. Consider a triangle A B C and let a , ba n dc denote the lengths of th...

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  5. In a triangle PQR, P is the largest angle and cosP=1/3. Further the in...

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  6. Let PQR be a triangle of area Delta with a = 2, b = 7/2 and c =5/2, wh...

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  7. If the angle A ,Ba n dC of a triangle are in an arithmetic propression...

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  8. Let A B C be a triangle such that /A C B=pi/6 and let a , ba n dc deno...

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  9. a triangle A B C with fixed base B C , the vertex A moves such that co...

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  10. Let A B Ca n dA B C ' be two non-congruent triangles with sides A B=4,...

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  11. A straight line through the vertex P of a triangle PQR intersects the ...

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  12. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  13. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  14. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  15. Internal bisector of /A of triangle ABC meets side BC at D. A line dra...

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  16. Given an isosceles triangle, whose one angle is-2pi/3 and the radius o...

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  17. In Delta ABC, which one is true among the following ?

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  18. Let a vertical tower A b have its end A on the level ground. Let C be ...

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  19. ABCD is a trapezium such that AB and CD are parallel and BC | CD. If ...

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  20. For a regular polygon, let r and R be the radii of the inscribed and ...

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  21. In triangle A B C , let /c=pi/2dot If r is the inradius and R is circu...

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