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The sides AB and AC of a triangle ABC ar...

The sides AB and AC of a triangle ABC are produced, and the bisectors of the external angles at B and C meet at P. Prove that if `AB gt AC`, then `PC gt PB`.

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ICSE-INEQUALITIES-EXERCISE 11
  1. Prove that the straight line joining the vertex of an isosceles triang...

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  2. In the following diagram, AD = AB and AE bisects angle A. Prove that :...

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  3. The sides AB and AC of a triangle ABC are produced, and the bisectors ...

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  4. In the following figure, AB is the largest side and BC is the smallest...

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  5. In quadrilateral ABCD, AB is the shortest side and DC is the longest s...

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  6. In triangle ABC, side AC is greater than side AB. If the internal bise...

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  7. In isosceles triangle ABC, sides AB and AC are equal. If point D lies ...

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  8. Given : ED = EC Prove : AB+AD gt BC.

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  9. In triangle ABC, AB gt AC and D is a point in side BC. Show that : AB ...

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  10. From the following figure, prove that : AB gt CD

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  11. In a triangle PQR, QR = PR and angleP=36^(@). Which is the largest sid...

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  12. If two sides of a triangle are 8 cm and 13 cm, then the length of the ...

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  13. In each of following figures, write BC, AC and CD in ascending order o...

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  14. Arrange the sides of DeltaBOC in descending order of their lengths. BO...

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  15. D is a point in side BC of triangle ABC. If AD gt AC, show that AB gt ...

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  16. In the following figure, angleBAC=60^(@)" and "angleABC=65^(@). Prov...

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  17. In the following figure , AC = CD, angleBAD=110^(@)" and " angleACB=...

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  18. From the following figure, prove that : (i) AB gt BD (ii) AC gt CD...

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  19. In a quadrilateral ABCD, prove that : (i) AB+BC+CD gt DA (ii) AB+B...

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  20. In the following figure, ABC is an equilateral triangle and P is any p...

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