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Exercis3

Exercise - 16

1. In  the bisector of  intersects the side AC at D. A line parallel to side AC intersects line segment AB, DB and CB at points P, R and Q respectively. Prove that

  1. AB X CQ = BC X AP
  2. PR X BQ = QR X BP

2. ABCD is a quadrilateral in which AB = AD. The bisector of intersects the side BC and CD respectively at E and F. Prove that the segment EF is parallel to the diagonal BD.

3. In and the bisector of  intersects AC at D. Prove that 

4. If the diagonal BD of a quadrilateral ABCD bisects both  show that 

5. D is the midpoint of side BC of  DE and DF are respectively bisectors ofsuch that E and F lie on AB and AC, respectively. Prove that EF || BC.

6. O is a point inside a The bisector of  meet the sides AB, BC and CA in points D, E and F respectively. Prove that AD. BE. CF = DB. EC. FA

7. In the adjoining figure, , AD is bisector of Prove that DE X (AB + AC) = AB X AC.

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

9. BO and CO are respectively the bisectors of AO is produced to meets BC at P. Show that

  1. AP is the bisector of 

 


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