Question Bank  Geometry  Hemant Malhotra

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

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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.

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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?

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Q39) 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?

Q40) In the figure given below, ABCD is a rectangle and GB = DH = 2HC. What is the area (in sq. cm) of the shaded region if AD = 1 cm and AB = 3 cm?

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Q42) A (1, 2) and B(1, 4) are two points and C is a moving point on the xaxis. What will be the xcoordinate of C when angle ACB is maximum

Method1 you will get 3 points
x = 1 , 7 , 3
so at 3 , angle is minimum i.e 0 degrees
again at x = 7 is a local maxima with angle less than 45 degrees
and at x = 1 global maximum as alpha angle is maximum with 45 degrees so at x=1 OA=1Method2 If a circle passes through A,B andC, then angle ACB will be maximum when radius of the circle is as small as possible
C = (k, 0)
AB is a chord, center of the circle pass through the perpendicular bisector of AB
equation will be x + y = 3
Center will be O (k, 3  k)
AO = CO
(k+ 1)^2 + (1  k)^2 = (3  k)^2
so k = 1, 7
radius is least for k=1

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Q44) Find the maximum area of a rectangle inscribed in a triangle with lengths 20, 24, 20.

Q45) In a triangle ABC, one side= 3, second side is double of third side. Find the maximum area of the triangle

Q46) A solid cube of side 1 cm is cut into two identical solid parts by a plane surface. The total surface area of both the solid parts is maximum possible. Two points are then selected on one of these solid parts. What is the maximum possible distance between these two points

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Q49) A school teacher played a game, ‘Geobasics’ with the students of a mathematics class by asking them to write a statement each on a piece of paper. The statements should be related to basics of geometry lesson that he taught last week to the class. He gave 3 points to a student, if the statement written by him/her is ‘always true’, 2 points, if the statement is ‘sometimes true’ and 1 point if the statement is ‘never true’.
What is the sum of the points given by the teacher to a group of five students who wrote the following statements:
(a) It is possible to draw three points that are noncoplanar.
(b) If two ants are walking along different straight lines but in different directions, their paths cannot cross more than once.
(c) If two rays share a common endpoint, then they form a line.
(d) Three coplanar lines may have zero, one, two or three points of intersection.
(e) If two planes intersect, they intersect in a straight line. 11
 13
 15
 Cannot be determined
 None of these.