In this page 10th grade geometry solution4 we are going to see solutions of some practice questions.

(9) In a triangle ABC,AD is the internal bisector of angle A, meeting BC at D.

(i) If BD = 2 cm, AB = 5 cm, DC =3 cm find AC.

Solution:

 Using “Angle bisector theorem” in the triangle ABC, we get (AB/AC) = (BD/DC) (5/AC) = (2/3) AC = (3 x 5)/2       = 15/2       = 7.5 cm

(ii) If AB = 5.6 cm, AC = 6 cm and DC = 3 cm find BC.

 Using “Angle bisector theorem” in the triangle ABC, we get (AB/AC) = (BD/DC) (5.6/6) = (BD/3) BD = (5.6 x 3)/6        = 16.8/6       = 2.8 cmFrom this we need to find the value of BC BC = BD + DC      = 2.8 + 3.    = 5.8 cm

(iii) If AB = x, AC = x – 2 cm, BD = x + 2 cm and DC = x – 1 find the value of x

 Using “Angle bisector theorem” in the triangle ABC, we get (AB/AC) = (BD/DC) [x/(x – 2)] = [(x + 2)/(x - 1)] x (x – 1) = (x + 2) (x – 2) x ² – x = x ² – 4 x² – x - x² + 4 = 0    - x + 4 = 0    - x = - 4      x = 4 cm The value of x is 4 cm

(10) Check whether AD is the bisector of angle A of the triangle ABC in each of the following.

(i) AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm

Solution:

 To check whether AD is the bisector of angle A of the triangle ABC, we have to check the following condition (AB/AC) = (BD/DC) (4/6) = (1.6/2.4) 0.66 = 0.66 From this we come to know that AD is the bisector of angle A of the triangle ABC.

(ii) AB = 6 cm, AC = 8 cm, BD = 1.5 cm and CD = 3 cm

Solution:

 To check whether AD is the bisector of angle A of the triangle ABC, we have to check the following condition (AB/AC) = (BD/DC) (6/8) = (1.5/3) 0.75 ≠ 0.5 From this we come to know that AD is not the bisector of angle A of the triangle ABC.