Q. 1. Let
and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC.(2)
Q. 2. In Fig., DE || AC and DF || AE. Prove that BF/EF = BE/EC (2)
Q. 3. ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2 (2)
Q. 4.Prove that the tangents drawn from the external point to the circles are equal. (2)
Q. 5. In an equilateral triangle ABC, D is a point on side BC such that BD =1/3 BC. Prove that, 9 AD2 = 7 AB2. (3)
Q. 6. O is any point inside a rectangle ABCD
(see Fig). 
Prove that OB2 + OD2 = OA2 + OC2. (3)
Q. 7. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. (4)
Q. 8. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (Pythagoras Theorem). (4)
Q. 9. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Prove this.(4)
Q. 10. Prove, In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (Pythagoras Theorem). (4)
