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Exercis2

Exercise - 15

1. The perpendicular AD on the base BC of a intersects BC at D so that DB = 3CD. Prove that 2AB2 = 2AC2 + BC2.

2. P and Q are points on the side CA and CB respectively of a right angled at C.

   Prove that AQ2 + BP2 = AB2 + PQ2.

3. In , if AD is the median, Show that AB2 + AC2 = 2(AD2 + BD2)

4. PQR is an isosceles right triangle, right angled at R. Prove that PQ2 = 2PR2.

5. In a  is an acute angle and  Prove that AC2 = AB2 + BC2 – 2BC. BD.

6. In the adjoining figure, find the length of BD, If 

7. Prove that the altitude of an equilateral triangle of side 

8. P and Q are the midpoint of the sides CA and CB respectively of right angled at C. Prove that 4(AQ2 + BP2) = 5AB2

9. In a triangle ABC, AD is perpendicular on BC. Prove that AB2 + CD2 = AC2 + BD2

10. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

11. In adjoining figure, OD, OE and OF are respectively perpendiculars to the sides BC, CA and AB from any point O in the interior of the triangle Prove that 
(i) OA2 + OB2 + OC2 – OD2 – OE2 – OF2 = AF2 + BD2 + CE2
(ii) AF2 + BD2+ CE2 = AE2 + CD2 + BF2

12. O is any point in the insertor of a rectangle ABCD. Prove that interior OB2 + OD2 = OC2 + OA2

Answers

(6) 13m

 


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