Math Assignment Ch6 Class X  Triangle
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Internal bisector of angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle. In Triangle ABC, if AD is the bisector of ∠A then \[\frac{AB}{AC}=\frac{BD}{DC}\]
Question 1: Q. 1. PA, QB and RC are each perpendicular to AC then \[Prove\; that\; \; \frac{1}{x}+\frac{1}{z}=\frac{1}{y}\] 
Question 2: If the bisector of an angle of triangle bisects the opposite side, then prove that the triangle is isosceles. 
Question 3: O is any point inside a triangle ABC. The bisectors of ∠AOB, ∠BOC and ∠COA meet the side AB, BC and CA in points D, E, F respectively. Show that AD X BE X CE = BD X EC X FA 
Question 4: In triangle ABC, AD is the internal bisector of ∠A which meets BC at point D. \[Prove\; that\; \frac{Ar(\Delta ABD)}{Ar(\Delta ACD)}=\frac{AB}{AC}\] 
Question 5: In the given figure express x in terms of a, b, c 
Question 6: Q6 The areas of two similar triangles are 81 cm^{2} and 49 cm^{2} respectively. Find the ratio of their corresponding heights? What is the ratio of their corresponding median. 
Question 7: In quadrilateral ABCD, ∠B = 90^{o} If AD^{2} = AB^{2} + BC^{2} = CD^{2} Prove that ∠ACD = 90^{o} 
Question 8: Prove that 8PT^{2} = 3PR^{2} + 5PS^{2}

Question 9: Triangle ABC is right angled at B , D is the mid point of BC. Prove that AC^{2} = 4AD^{2}  3AB^{2} 
Question 10: In triangle ABC, AD ⟂ BC and point D lies on BC such that 2BD = 3CD, Prove that 5AB^{2} = 5AC^{2} +BC^{2} 
Question 11: △ABC is right angled at C. Let BC = a, CA = b, BC = c, and let p be the length of perpendicular from C on AB Prove That :

Question 12: In △ABC, P and Q are the points on sides CA and CB respectively, which divides these sides in 2 : 1. Prove that (i) 9AQ^{2} = 9AC^{2} + 4BC^{2} ^{} (ii) 9BP^{2} = 9BC^{2} + 4AC^{2} ^{} (iii) 13AB^{2 }= 9(AQ^{2} + BP^{2})

Question 13: In △ABC, AC > AB, D is the mid  point of BC and AE⟂BC . 
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