Page 241 - Ganit Kaushal

Miscellaneous Solved Examples

There are four options (Q. 1 to Q. 3), out of which only one is correct. Choose the correct option.
Ex 1. ABCD is a rectangle, BD and CA are its diagonals, and ∠BDC = 37°. Then A B
∠ABD is equal to
(a) 53° (b) 37° O

(c) 47° (d) 57° 37°
Sol. (b) [ they are alternate angles, so they are equal] D C
Ex 2. AB and CD are diameters of a circle making an angle of 90° with each other as C
shown in the adjacent figure. If AC is 6 cm, then BC is equal to
(a) 4 cm (b) 5 cm A 6 cm 90° B
(c) 6 cm (d) 12 cm

Sol. (c) [ CD is the perpendicular bisector of AB. \ AC = BC] D
Ex 3. How many geometrical shapes are required to construct the artwork ‘A Person’?
(a) One (b) Two (c) Three (d) Four

Sol. (c) [ Arc, straight line, and circle; a total of 3.]
Ex 4. Fill in the blanks.
(a) The perpendicular bisector of any chord (other than the diameter) of the circle passes through the
_______ of the circle.
(b) The diameter of a circle is _______ its radius.
Sol. (a) centre (b) twice
Ex 5. State whether the following statements are True (T) or False (F).

(a) Perpendicular bisectors of any two chords (other than the diameter) of a circle meet at the centre
of the circle.

(b) It is impossible to construct a closed four-sided figure in which all the angles are 90° and opposite
sides are not equal.

(c) It is impossible to construct a 4-sided figure in which all sides are equal, but it is not a square.
Sol. (a) True (b) True (c) False [see construction-22]

Miscellaneous Exercise 8.5

1. Identify if there are any squares in this collection. Use measurements if needed. (NCERT)

A B C D
2. Draw a rectangle of sides 2 cm and 10 cm. After drawing, check if it satisfies both the rectangle
properties R1 and R2. (NCERT)

Playing with Constructions 239