Download App

Circles — Maths STD 9 — Question

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

 A farmer has a circular garden as shown in the picture above. He has a different type of trees, plants and flower plants in his garden. In the garden, there are two mango trees $A$ and $B$ at a distance of $AB = 10m.$ Similarly, he has two Ashoka trees at the same distance of $10\ m$ as shown at $C$ and $D.\  AB$ subtends $\angle\text{AOB}=120^\circ$ at the center $O,$ The perpendicular distance of $AC$ from center is $5m$. The radius of the circle is $13\ m$. Now answer the following questions:
$i.$ What is the value of $\angle\text{COD}?$
$a. 60^\circ $
$b. 120^\circ $
$c. 100^\circ $
$d. 80^\circ $
$ii.$ What is the distance between mango tree $A$ and Ashok tree $C?$
$a. 12\ m$
$b. 24\ m$
$c. 13\ m$
$d. 15\ m$
$iii.$ What is the value of $\angle\text{OAB}?$
$a. 60^\circ $
$b. 120^\circ $
$c. 30^\circ $
$d. 90^\circ $
$iv.$ What is the value of $\angle\text{OCD?}$
$a. 30^\circ $
$b. 120^\circ $
$c. 60^\circ $
$d. 90^\circ $
$v.$ What is the value of $\angle\text{ODC}?$
$a. 90^\circ $
$b. 120^\circ $
$c. 60^\circ $
$d. 30^\circ $
✓

Answer

$(i)$ $(b)$ $120^\circ $
$(ii)$ $(b)$ $24m$
$(iii)$ $(c)$ $30^\circ $
$(iv)$ $(a)$ $30^\circ $
$(v)$ $(d)$ $30^\circ $

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Case study (4 Marks)" from Circles→Circles — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

Following bar graph represents the sales of cold drinks of two companies A and B from 2015 to 2018.
Image
Read the above bar graph and answer the following questions:
(i) The year in which the difference between the sales of two companies was highest, was
(a) 2018$\quad$ (b) 2015$\quad$ (c) 2016$\quad$ (d) 2017$\quad$
(ii) Total sales of A and B in the year 2016 was
(a) 116,000 units$\quad$ (b) 127,000 units$\quad$ (c) 138,000 units$\quad$ (d) 149,000 units
(iii) The minimum difference between the sales of company A and B in any year in the given period was
(a) 9,000 units$\quad$ (b) 7,000 units$\quad$ (c) 5,000 units$\quad$ (d) 3,000 units
(iv) In which year was the sales of company B more than the sales of company A?
(a) 2015$\quad$ (b) 2016$\quad$ (c) 2017$\quad$ d) 2018
(v) The ratio of the total sales in the year 2017 and that in 2018 was
a) 107:145$\quad$ (b) 29:36$\quad$ (c) 127: 145$\quad$ (d) 107: 127

→
Our excessive dependence on motorized road transport imposes significant economic costs on society. These include congestion, road casualties, physical inactivity and ill health caused by it eg.: obesity. Cycling could substantially reduce these risks, while strengthening local economies in both urban and rural areas, supporting local businesses and boosting the economic productivity.
A bicycle is being lent at fixed charges for the first three days of week and an additional charge of each day thereafter. If fixed charges are ₹ x and per day charges are ₹ y, then based on the above information, answer the following questions:
(i) Form the linear equation, if Mr. Sam paid ₹ 27 for a bicycle kept for 7 days.
(ii) Form the linear equation, if Mr. David paid ₹30 for a bicycle kept for 6 days.
(iii) If fixed charge is ₹ 15, then find the additional charge paid by Mr. Sam for each extra day.
(iv) If per day charge for lending the bicycle is ₹ 3, find the value of fixed charge paid by Mr. David.
→
Read the Source/ Text given below and answer these questions:

There is a square park $\text{ABCD}$ in the middle of Saket colony in Delhi.Four children Deepak, Ashok, Arjun and Deepa went to play with their balls. The colour of the ball of Ashok, Deepak, Arjun and Deepa are red, blue, yellow and green respectively. All four children roll their ball from centre point $O$ in the direction of $XOY, X'OY, X'OY'$ and $XOY'.$ Their balls stopped as shown in the above image. Answer the following questions:
$i.$ What are the coordinates of the ball of Ashok$?$
$a. (4, 3)$
$b. (3, 4)$
$c. (4, 4)$
$d. (3, 3)$
$ii.$ What are the coordinates of the ball of Deepa$?$
$a. (2, -3)$
$b. (3, 2)$
$c. (2, 3)$
$d. (2, 2)$
$iii.$ What the line $\text{XOX'}$ is called$?$
$a. y-$axis.
$b.$ ordinate.
$c. x-$axis.
$d.$ origin.
$iv.$  What the point $O(0, 0)$ is called$?$
$y-$axis.
ordinate.
$x-$axis.
origin.
$v.$ What is the ordinate of the ball of Arjun$?$
$a. -3$
$b. 3$
$c. 4$
$d. 2$
→
Read the Source/ Text given below and answer these questions:

Ashok is studying in $9^{th}$ class in Govt School, Chhatarpur. Once he was at his home and was doing his geometry homework. He was trying to measure three angles of a triangle using the Dee, but his dee was old and his Dee's numbers were erased and the lines on the dee were visible. Let us help Ashok to find the angles of the triangle. He found that the second angle of the triangle was three times as large as the first. The measure of the third angle is double of the first angle. Now answer the following questions:
$i.$ What was the value of the first angle$?$
$a. 30^\circ $
$b. 45^\circ $
$c. 60^\circ $
$d. 90^\circ $
$ii.$ What was the value of the third angle$?$
$a.30^\circ $
$b.45^\circ $
$c.60^\circ $
$d. 90^\circ $
$iii.$ What was the value of the second angle$?$
$a.30^\circ $
$45^\circ $
$c.60^\circ $
$d. 90^\circ $
$iv.$ What was the value of $\angle4$ as shown the figure$?$
$a.120^\circ $
$b.45^\circ $
$c.60^\circ $
$d. 90^\circ $
$v.$  What was the sum of all three angles measured by Ashok using Dee$?$
$a.270^\circ $
$b.180^\circ $
$c.100^\circ $
$d. 90^\circ $
→
Deep draws the spiral of irrational numbers below on a paper.
Image
4. What is the length of $OE$ in the spiral$?$
5. Simplify:
A.$ -1$
B. $\sqrt{3}-\sqrt{5}$
C. $-4+\sqrt{15}$
D. $4-2 \sqrt{ } 15$
→
Read the Source/ Text given below and answer these questions:
In the above picture, one small square is of size $1\ km \times 1\ km.$ From the starting point $O(0, 0)$ Deepak started to drive towards his home. He first drives $3\ km$ in left then he turned to his left and drove $2\ km,$ there he found a temple. He worshipped there and drove $6\ km$ in the left direction, there is a zoo and from the zoo, he drives $2\ km$ on the right side, then he reached his home. From $O$ Sanjay drove for his school, he drove $1\ km$ to his right then took a left turn and drives $2\ km$ then again took a right turn and drives $2\ km$. He found a hospital in the way. From Hospital he drove $3\ km$ and finally reached his school.
$i.$ What are the coordinates of the Hospital?
$a. (3, 2)$
$b. (2, 3)$
$c. (3, 3)$
$d. (5, 5)$
$ii.$ What is common abscissa of school, Hospital, Zoo and Deepak's home$?$
$a. 3$
$b. 5$
$c. -3$
$d. -5$
$iii.$ What is the common ordinate of temple and Zoo$?$
$a. 3$
$b. 5$
$c. -3$
$d. -2$
$iv.$ Deepak Drove in which quadrants$?$
$a. I$ and $II$
$b. II$ and $III$
$c. III$ and $IV$
$d. IV$ and $I$
$v.$ Sanjay Drove in which quadrants$?$
$a. I$ only
$b. II$ and $III$
$c. III$ and $IV$
$d. II$ and $I$
→
'Learning by doing' has great impact in teaching of Maths. Students also enjoy Mathematics by activity method. Mr. Paul, a Mathematics teacher has explained the topic of Lines and Angles by taking a very thin steel wire. He used steel wire and made some shapes at some specific angles and shown to students and asked questions.
Image
Choose the correct option in the following questions:
(i) What is the measure of $\angle B O D$ in figure?
(a) $90^{\circ}$$\quad$(b) $70^{\circ}$$\quad$(c) $80^{\circ}$$\quad$(d) $100^{\circ}$
(ii) What is measure of $\angle y$ in figure ?
(a) $110^{\circ}$$\quad$(b) $90^{\circ}$$\quad$(c) $140^{\circ}$$\quad$(d) $100^{\circ}$$\quad$
(iii) What is the measure of $\angle a$ and $\angle b$ respectively in Figure, if a : b = 2 : 3 and $O P \perp X Y$ ?
(a) $54^{\circ}, 36^{\circ}$$\quad$(b) $36^{\circ}, 54^{\circ}$$\quad$(c) $60^{\circ}, 90^{\circ}$$\quad$(d) $40^{\circ}, 60^{\circ}$
(iv) What is measure of $\angle c$ in figure ?
(a) $144^{\circ}$$\quad$(b) $90^{\circ}$$\quad$(c) $126^{\circ}$$\quad$(d) $120^{\circ}$
→
→
Read the following text carefully and answer the questions that follow:
Haresh and Deep were trying to prove a theorem. For this they did the following
Image
$i.$ Draw a triangle $ABC$
$ii. \ D$ and E are found as the mid points of $AB$ and $AC$
$iii.\ DE$ was joined and $DE$ was extended to $F$ so $DE = EF$
$iv. \ FC$ was joined.
Questions :
$i. \triangle ADE$ and $\triangle EFC$ are congruent by which criteria?
$ii.$ Show that $C F \| A B$.
$iii.$ Show that $C F=B D$.
OR
Show that $D F=B C$ and $D F \| B C$.
→
Read the Source/ Text given below and answer these questions: In the middle of the city, there was a park $\text{ABCD}$ in the form of a parallelogram form so that $AB = CD, AB \| CD$ and $AD = BC, AD \| BC$ Municipality converted this park into a rectangular form by adding land in the form of $\triangle\text{APD}$ and $\triangle\text{BCQ}.$ Both the triangular shape of land were covered by planting flower plants.

Answer the following questions:
$i.$ What is the value of $\angle\text{x}?$
$a. 110^\circ $
$b. 70^\circ $
$c. 90^\circ $
$d. 100^\circ $
$ii. \triangle\text{APD}$ and $\triangle\text{BCQ}$ are congruent by which criteria?
$a. \text{SSS}$
$b. \text{SAS}$
$c. \text{ASA}$
$d. \text{RHS}$
$iii.PD$ is equal to which side$?$
$a. DC$
$b. AB$
$c. BC$
$d. BQ$
$iv. \triangle\text{ABC}$ and $\triangle\text{ACD}$ are congruent by which criteria?
$a. \text{SSS}$
$b. \text{SAS}$
$c. \text{ASA}$
$d. \text{RHS}$
$v.$ What is the value of $\angle\text{m}?$
$a. 110^\circ $
$b. 70^\circ $
$c. 90^\circ $
$d. 20^\circ $
→