Question Bank  Geometry  Shashank Prabhu, CAT 100 Percentiler

Q38) In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with center B) is drawn. If the circle cuts AB and BC at P and Q respectively, the AP:QC is equal to
[OA: 3 : 8]

Q39) How many integers may be the measure, in degrees, of the angles of a regular polygon?
[OA: 22]

Q54) One side of a triangle has length 75. Of the other two sides, the length of one is double the length of the other. What is the maximum possible area for this triangle?
[OA: 1875]

Q61) A circle cuts a square at 8 distinct points such that each side of the square contains a chord of the
circle equal to the length of the radius of the circle. Find the ratio of the area of the circle to that of
the square.[OA: π : 3]

Q63) ABCD is a cyclic isosceles trapezium where AD and BC are the two parallel sides and the lengths of the sides AB, AD and BC are in the ratio 4 : 4 : 5. What is the ratio AD : AC?
a. 2 : 5
b. 2 : 3
c. 4 : 5
d. 4 : 7[OA: Option b]

Q68)In the figure given below, PQRS is a rectangle. If PT = 16 cm, QT = 24 cm and angle PTQ = 90 what
is the area (in cm^2) of the rectangle PQRS?[OA: 384]

Q69) A line x + y = 14 cuts the curve y = x^2 + 4x at two distinct points. What type of triangle will be formed by joining these two points to a third point (1, 20)?
[OA: Isosceles]

Q84) Find the sum of the digits of both the coordinates of the point on the xaxis which is equidistant from the points (49, 52) and (35, 60).
[OA: 1]

Q94) Points A(–2, 9) and B(6, 3) lie on the circumference of a circle whose radius is an integer. Which of the following cannot be the length of the radius?
a. 3
b. 5
c. 6
d. 9[OA: Option a]

Q96) From a rectangular sheet of dimensions 30 cm × 20 cm, four squares of equal size are cut from the four corners. Then the resulting four sides are bent upwards to give it the shape of an open box. If the volume of the box is 1056 cm^3, what is the length of the side of the squares cut from the corners?
[OA: 4]