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O is any point in the exterior of a Delt...

O is any point in the exterior of a `DeltaABC`. Prove that `2(OA + OB + OC) > (AB + BC + CA)`
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O is any point in the interior of triangleABC such that OB=OC and AB=AC. Show that AO bisects angleA .

D is any point on the base BC, produced of an isosceles triangle ABC, prove that AD>AB.

O is any point inside a rectangle ABCD (see Fig. 6.52). Prove that OB^2 + OD^2 = OA^2 + OC^2 .

In fig., O is a point in the interior of a triangle ABC, OD bot BC, OE bot AC and OF bot AB. Show that:- OA^2+OB^2+OC^2-OD^2-OE^2-OF^2=AF^2+BD^2+CE^2 .

If O is the circumcentre, G is the centroid and O' the orthocenter of DeltaABC prove that (i) SA+SB+SC=3SG, where S is any point in the plane of DeltaABC . (ii) OA+OB+OC=OO' Where, AP is diameter of the circumcircle.

If G be the centroid of a triangle ABC, prove that, AB^2+BC^2+CA^2=3(GA^2+GB^2+GC^2)

If O and H be the circumcentre and orthocentre respectively of triangle ABC, prove that vec OA+ vec OB+ vec OC= vec OH .

AD is a median of DeltaABC . Is AB + BC + CA gt 2AD ?

Draw any circle and mark: a point in its exterior

D and E are points on sides AB and AC respectively of DeltaABC such that ar (DBC) = ar (EBC). Prove that DE II BC .

MBD-Triangles-Exercise
  1. Of all the line segments drawn from a point P to a line l not containi...

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  2. In DeltaABC, AC > AB. The bisector of angleA meets BC at D. Prove that...

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  3. O is any point in the exterior of a DeltaABC. Prove that 2(OA + OB + O...

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  4. Prove that the difference of any two sides of a triangle is less than ...

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  5. In Fig. , PQR is a triangle, S is any point in its interior, show tha...

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  6. In Fig. , AB > AC, show that AB > AD.

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  7. Find x+y+z

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  8. Diagonals PR and QS of a quadrilateral PQRS intersect each other at O....

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  9. Diagonals PR and QS of a quadrilateral PQRS intersect each other at O....

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  10. In Fig. , AP is the shortest line-segment that can be drawn from A t...

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  11. If two sides of a triangle are unequal, then larger side has a smaller...

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  12. If two angles of a triangle are unequal, then greater angle has the la...

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  13. Sum of any two sides of a triangle is greater than the third side.

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  14. Difference of any two sides of a triangle is equal to the third side.

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  15. Of all the line-segments that can be drawn from a point to a line not ...

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  16. Sum of the three sides of a triangle is less than the sum of its three...

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  17. Sum of any two sides of a triangle is ........... than the third side.

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  18. If two angles of a triangle are unequal, then smaller angle has the .....

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  19. Of all line-segments drawn from a point to a line not containing it th...

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  20. Difference of any two sides of a triangle is ...... Than third side.

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