# Question Bank - Geometry - Hemant Malhotra

• Q24) In an art class the teacher tells the students to draw the largest circle possible on a piece of paper in the shape of a square and then draw a rectangle lying between the circumference of the circle and the edge of the square such that a corner of the rectangle lies on the circumference of the circle and two sides of the rectangle coincide with those of the square. If the rectangle measures 10 cm × 20 cm then what is the area of the sheet of paper?

• Q25) A circle circumscribes a regular hexagon H1 and is inscribed inside a regular hexagon H2. What is the ratio of the areas of H1 and H2?

• Q26) In a triangle ABC with AB = 14 cm, D and E are points on BC and AC respectively such that BE and AD intersect at point F and the area of ∆ BFD = area of ∆ AFE. Also BD:DC = 2:5. Find the length of DE. • Q27) • Q28) If the sum of lengths of three sides of a rectangle is 100 units, then find the maximum possible area of the rectangle ?

• Q29) • Q30) Five equal squares are joined together to form a rectangle whose perimeter is 372. What is the area of one square?

• Q31) 3 identical right angle cones with base radius r are placed on their bases so that each is touching the other two.The radius of circle drawn through their vertices is:-
a. smaller than r
b. Equal to r
c. larger than r
d. Depends on height

• It's like three circles touching each other & when u meet center it will form equilateral triangle with side 2r .. and Radius of circle going through it will be equal to circumradius = 2r/sqrt3 so greater then r

• Q32) • Q33) • Q34) • Q35) In the figure given below, seg EQ is the bisector of angle FEG. Seg EQ is perpendicular to side FG, seg QP is perpendicular to side FE and seg QR is perpendicular to side EG. Find EP x PF, if ER = 23 cm and RG = 13 cm. • Q36) • Q37) In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 17. What is the greatest possible perimeter of the triangle?

• Q38) 45

138

45

68

62

61

30