Quant Boosters - Geometry - Raman Sharma - Set 2


  • Faculty and Content Developer at TathaGat


    Credits : Sahabudeen Salaeh

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  • Faculty and Content Developer at TathaGat


    Q4) A semicircle is inscribed in an equilateral triangle as shown. What fraction of the triangle lies inside the semicircle?

    0_1507021773450_34e768d2-4ab9-4fa8-94ce-2c2721ce2e3c-12592349_885557224895243_5455117907032341670_n.jpg

    [OA: √3π/8 ]


  • Faculty and Content Developer at TathaGat


    Q5) In ∆ABC , AD ia the altitude from A onto the side BC. If b > c , angle C =23° and AD = abc/(b² - c²) , then angle B is equal to
    a. 83°
    b. 113°
    c. 123°
    d. 75°
    e. NoT

    [OA: 113]


  • Faculty and Content Developer at TathaGat


    Q6) On a circle 26 equidistant points are marked. These points are joined to form triangles. Of the triangles formed, how many of them will have their circumcenter on one of their sides?

    [OA : 312]


  • Faculty and Content Developer at TathaGat


    Q7) ABCD is a square with side length r units .
    AB is trisected by two points R and S ,
    CD is trisected by two points P and Q ,
    AP and DR intersect at E
    AP and DS intersect at N
    AQ and DR intersect at M
    AQ and DS intersect at F
    What is the area of the quadrilateral EMFN ?

    [OA: (r/6)^2]


  • Faculty and Content Developer at TathaGat


    Credits : Turan Bey

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  • Faculty and Content Developer at TathaGat


    Q8) In the square ABCD , a line through B intersects the extension of CD at E , the side AD at F and the diagonal AC at G if BG = 9 and GF = 3 , then what is the length of EF ?

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    [OA: 24]


  • Faculty and Content Developer at TathaGat


    Q9) Two of the sides of a triangle are in the ratio 3:4. The medians to these sides are perpendicular to each other. If the third side of the triangle is 12root(5), find the smaller of the first two sides of the triangle.

    [OA: 36]


  • Faculty and Content Developer at TathaGat


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  • Faculty and Content Developer at TathaGat


    Q10) The shortest median of a right-angled triangle is 25 units. If the area of the triangle is 336 sq.units, what is the length (in units) of the longest median of the triangle?

    [OA: 48.5]


  • Faculty and Content Developer at TathaGat


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  • Faculty and Content Developer at TathaGat


    Q11) In triangle ABC, two lines DE and FG are drawn parallel to BC such that they divide AC in the ratio 2:3:5. Find the ratio of area of triangle ABC to area of the trapezium DEGF.

    [OA: 100 : 21]


  • Faculty and Content Developer at TathaGat


    Q12) The parallel sides of Trapezium is 6 and 8 units respectively. Find the length of the line segment parallel to these sides and which divides the area of trapezium in equal halves.
    A. 4 √3
    B. 5 √ 2
    C. 7
    D. 7/√2

    [OA: Option b]


  • Faculty and Content Developer at TathaGat


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  • Faculty and Content Developer at TathaGat


    credits : @swetabh_kumar

    let length be x..so 1/2 * (6x) * h1= 1/2 * (1/2 * 14 * h2)..h1 is the height of the smaller trapezium...h2 is overall heght.
    so (6+x)h1=7h2
    now the line of legth x is divided into length 6 and 2 equal corner segments of legth (x-6)/2 each.
    by similar triangles, h1/h2= (x-6)/2.
    plug in the 1st eqn7/(6+x)=(x-6)/2
    x^2 - 36 = 14
    x = 5 root 2


  • Faculty and Content Developer at TathaGat


    Q13) What is the ratio of area of a regular dodecagon (a polygon with 12 sides) to the area of a regular hexagon if both the polygons are inscribed in the same circle?

    [OA: 2 : √3]


  • Faculty and Content Developer at TathaGat


    Q14) In a triangle ABC AB = AC and angle BAC = 100°. AB is produced to D such that AD = BC. find angle BCD.

    0_1507023001662_b34be995-0ba4-491c-9880-b670e13743f3-12243263_850941525023480_7604062874007029589_n.jpg

    [OA: 10]


  • Faculty and Content Developer at TathaGat


    Q15) There are 7 smaller squares inside the large rectangle. If the green square has side length 1 and the brown square has side length 2, what is the area of the rectangle?

    0_1507023098227_7d6309ea-0a97-44de-9f49-7f47e8ca0855-13507198_979022148882083_1259985714960540843_n.jpg

    [OA: 63]


  • Faculty and Content Developer at TathaGat


    Q16) Let ABCDE be a regular pentagon. Construct an equilateral triangle PAB with point P inside the pentagon. Find the measure of the angle PCE.

    [OA: 6]


  • Faculty and Content Developer at TathaGat


    Q17) QR = ?

    0_1507023649129_5e563d29-64ef-4529-a45c-3ee0cef47420-20046307_1337438329707128_5854284451029036500_n.jpg

    [OA: 18]


 

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