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Circles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsCircles4 Marks
Question
Read the Source Text given below and answer these questions:

 There was a circular park in Defence colony At Delhi. For fencing purpose Poles $A, B, C$ and $D$ were installed at the circumference of the park. Ram tied wires From $A$ to $B$ to $C$ and $C$ to $D,$ He managed to measure the $\angle\text{A}=100^\circ$ and $\angle\text{D}=80^\circ$ The point $O$ in the middle of the park is the center of the circle. Now answer the following questions:
$i.$ What is the value of $\angle\text{B}?$
$a. 80^\circ $
$b. 100^\circ $
$c. 90^\circ $
$d. 70^\circ $
$ii.$ What is the value of $\angle\text{C}?$
$a. 80^\circ $
$b. 100^\circ $
$c. 90^\circ $
$d. 70^\circ $
$iii.$ What is the special type of quadrilateral $\text{ABCD}?$
$a.$ Square.
$b.$ Rectangle.
$c.$ Cyclic quadrilateral.
$d.$ Trapezium.
$iv.$ What is the property of cyclic quadrilateral?
$a.$ Opposite angles are supplementary.
$b.$ Adjacent angles are equal.
$c.$ Opposite angles are equal.
$d.$ Adjacent angles are complementary.
$v.$ What you will call the yellow shaded shape $\text{OBC}?$
$a.$ Segment.
$b.$ Arc.
$c.$ Chord.
$d.$ Sector.
✓

Answer

$(i)$ $(b)$ $100^\circ $
$(ii)$ $(a)$ $80^\circ $
$(iii)$ $(c)$ Cyclic quadrilateral.
$(iv)$ $(a)$ Opposite angles are supplementary.
$(v)$ $(d)$ Sector.

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