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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 mid-points 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= 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)

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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