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I is the incentre of Delta ABC, Produced...

I is the incentre of `Delta ABC`, Produced AI bisects BC at D. Prove that `Delta ABC` is isosceles.

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O is the circumcentre of Delta ABC and OD bot BC . Prove that angle BOD= angle BAC

I is the centre of the incircle of Delta ABC, produced AI intersects the circumercile of that triangle at the point P. Prove that PB=PC=PI

I is the incentre of the Delta ABC . The perpendicular drawn from I to BC intersects BC at. P. Prove that AB-AC=BP-CP .

In Delta ABC,AB= AC and E is any point on the extended BC. The circumeircel of Delta ABC intersects AE at the point D. Prove that angle ACD= angle AEC .

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S is the centre of the circumcircle of Delta ABC and if AD bot BC , prove that angle BAD= angle SAC .

BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.

In a triangle ABC, AD is the median drawn on the side BC is produced to E such that AD = ED prove that ABEC is a parallelogram.

If the bisector of an angle of a triangle also bisects the opposite side, prove that the triangle is isosceles.

CALCUTTA BOOK HOUSE-THEOREMS ON CONCURRENCE-EXERCISE Long-answer type questions
  1. Find the value of k for which the given value is a solution of the giv...

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  2. Determine the nature of the roots of following quadratic equations : (...

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  3. Some students planned a picnic. The budget for food was Rs. 480. But e...

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  4. Find the value of k for which the given value is a solution of the giv...

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  5. A piece of cloth costs Rs. 35. If the piece were 4 m longer and each m...

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  6. Two medians BE and CF of Delta ABC intersect at G. Prove that area of ...

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  7. I is the incentre of Delta ABC, Produced AI bisects BC at D. Prove tha...

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  8. Find the values of k for which the roots are real and equal in the fol...

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  9. I is the incentre of the Delta ABC. The perpendicular drawn from I to ...

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  10. Find the values of k for which the roots are real and equal in the fol...

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  11. E is the mid-point of AD, a median of the Delta ABC. The extended BE i...

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  12. Write the first five terms of the following sequence whose nth term ar...

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  13. In Delta ABC, angle B le angle C. If the interior bisector of angle B...

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  14. P is a point on the median AD of the Delta ABC. Prove that area of De...

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  15. Find the next five terms of each of the following sequences given by :...

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  16. Write the first five terms of the following sequence whose nth term ar...

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  17. A bag contains 3 red balls, 5 black balls and 4 white balls. A ball is...

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