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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?
A
75
B
90
C
120
D
150
Question 1 Explanation: 
105
We know that BP=AB and thus since angle PBC = 60o
Thus angle ABP = 30o and angle BAP = (180-30)/2 = 75o
Angle DAP = 90-75 = 15.
Thus angle APD = 180-2x15 = 1500
Correct answer is (d)
Question 2
The points of intersection of three lines 2X +3Y -5 =0 5X -7Y +2 = 0 And 9X -5Y -4 =0
A
Form a triangle
B
Are on lines perpendicular to each other
C
Are on lines parallel to each other
D
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)
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 mid-points of the sides AB and BC.
A
4√2
B
5
C
3.5
D
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 ΔCBE to that of the triangle ΔADE?
A
1: 4
B
1: 2
C
1: 3
D
Data insufficient
Question 4 Explanation: 
107
The area of the triangle is directly proportional to the square of the bases.
Since the ratio of the length = 1:2
Therefore, the area should be in the ratio of 1:4.
Correct option is (a)
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? 108
A
120
B
66
C
93
D
87
Question 5 Explanation: 
Now let us consider the circle with center Q.
EQ= 20-EF = 8 and also PE = 8
Similarly PA=BR =20- AB = 15
QO=CR = 20-10 = 10.
The perimeter of the triangle PQR = 2x(8+15+10)+5+10+12 = 93
Correct option is (c)
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