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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:

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
 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:

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?
 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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