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Prove that the internal bisectors of the...

Prove that the internal bisectors of the angles of a triangle are concurrent

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Show that the perpendicular bisectors of the sides of a triangle are concurrent.

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Prove that the angle between internal bisector of one base angle and the external bisector of the other base angle of a triangle is equal to one-half of the vertical angle.

Prove that the angle between internal bisector of one base angle and the external bisector of the other base angle of a triangle is equal to one half of the vertical angle.

Prove that the bisector of the vertical angle of an isosceles triangle bisects the base at right angles.

Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.

Show that the perpendicular bisectors of the sides of the triangle with vertices (7, 2), (5, -2) and (-1, 0) are concurrent. Also find the coordinates of the point of concurrence (circumcentre).

NAVNEET PUBLICATION - MAHARASHTRA BOARD-QUESTION BANK 2021-VECTOR AND THREE DIMENSIONAL GEOMETRY
  1. Find the centroid of tetrahedron with vertices K(5, -7, 0), L(1, 5, 3)...

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  2. If a line has the direction ratios 4, -12, 18, then its direction cos...

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  3. Show that the points A(2, -1, 0) B(-3, 0, 4), C(-1, -1, 4) and D(0, -5...

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  4. Using properties of scalar triple product, prove that [(bar(a) + bar(b...

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  5. The direction ratios of AB are -2,2,1. If A -= (4,1,5) and l(AB) = 6 u...

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  6. If G(a,2,-1) is the centroid of the triangle with vertices P(1,3,2),Q(...

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  7. If G(r, (-4)/(3), (1)/(3)) is centroid of the triangle having vertices...

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  8. Prove that an angle inscribed in a semi-circle is a right angle usi...

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  9. Prove using vectors: Medians of a triangle are concurrent.

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  10. Show that the perpendicular bisectors of the sides of a triangle are c...

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  11. Express -hat(i)-3hat(j)+4hat(k) as the linear combination of the vecto...

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  12. If Q be the foot of perpendicular from P(2, 4, 3) on the line joining ...

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  13. Prove that the internal bisectors of the angles of a triangle are conc...

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  14. Using vector method, find the incenter of the triangle whose vertices ...

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  15. The angle between the lines whose direction cosines l, m, n satisfy t...

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  16. If A (bara) and B (barb) are any two points in the space and R(b...

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  17. D,E divide sides BC and CA of a triangle ABC in the ratio 2:3 respecti...

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  18. D,E divide sides BC and CA of a triangle ABC in the ratio 2:3 respecti...

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  19. Find the value of a tetrahedrn whose vertices are A(-1,2,3),B(3,-2,1),...

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  20. If four points A (overset(-)a), B(overset(-)b), C (overset(-)c) & D(o...

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