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Geometry and Mensuration: Level 3 Test 2
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Question 1 
An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in digress?
75  
90  
120  
150

Question 2 
The points of intersection of three lines
2X +3Y 5 =0
5X 7Y +2 = 0
And 9X 5Y 4 =0
Form a triangle  
Are on lines perpendicular to each other  
Are on lines parallel to each other
 
Are coincident 
Question 2 Explanation:
The points of intersection of the three graphs are : (1,1)
( If only two pairs of equations are solved one
can find that only one possible solution exists)
Thus correct option is (d)
( If only two pairs of equations are solved one
can find that only one possible solution exists)
Thus correct option is (d)
Question 3 
In the given figure, EADF is a rectangle and ABC is a triangle whose vertices lie on the sides of EADF. AE =22, BE= 6, CF =16 and BF =2. Find the length of the line joining the midpoints of the sides AB and BC.
4âˆš2  
5
 
3.5  
None of these 
Question 3 Explanation:
$\displaystyle \begin{array}{l}The\text{ }length\text{ }of\text{ }the\text{ }line\text{ }joining\text{ }the\text{ }mid\text{ }point\text{ }of\text{ }AB\text{ }and\text{ }BC\text{ }=1/2\text{ }of\text{ }AC\\\sqrt{{{6}^{2}}+{{8}^{2}}}=5cm\end{array}$
Question 4 
In the adjoining figure, points A, B, C and D lie on the circle. AD= 24 and BC= 12. What is the ratio of the area of Î”CBE to that of the triangle Î”ADE?
1: 4
 
1: 2  
1: 3  
Data insufficient 
Question 5 
Below shown are three circles, each of radius 20 and centers at P, Q and R; further AB= 5, CO 10 and EF= 12. What is the perimeter of the triangle PQR?
120  
66
 
93  
87 
Question 5 Explanation:
Now let us consider the circle with center Q.
EQ= 20EF = 8 and also PE = 8
Similarly PA=BR =20 AB = 15
QO=CR = 2010 = 10.
The perimeter of the triangle PQR = 2x(8+15+10)+5+10+12 = 93
Correct option is (c)
EQ= 20EF = 8 and also PE = 8
Similarly PA=BR =20 AB = 15
QO=CR = 2010 = 10.
The perimeter of the triangle PQR = 2x(8+15+10)+5+10+12 = 93
Correct option is (c)
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