Download App

Circles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsCircles4 Marks
Question

Prem did an activity on tangents drawn to a circle from an external point using 2 straws and a nail for maths project as shown in figure.

Based on the above information, answer the following questions.
  1. Number of tangents that can be drawn to a circle from an external point is:
  2. On the basis of which of the following congruency criterion, $\triangle\text{OAP}\cong\triangle\text{OBP}?$
  3. $\text{If }\angle\text{AOB}=150^\circ,\text{then }\angle\text{APB}=$
    Or
    $\text{If }\angle\text{APB}=40^\circ,\text{then }\angle\text{BAO}=$
✓

Answer

1. 22. RHS
3. 30º
Or
20º
 

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 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

A ball is thrown in the air so that $t$ seconds after it is thrown, its height $h$ metre above its starting point is given by the polynomial $h=25 t-5 t^2$.
Image
Observe the graph of the polynomial and answer the following questions:
$(i)$ Write zeroes of the given polynomial.
$(ii)$ Find the maximum height achieved by ball.
$(iii) (a)$ After throwing upward, how much time did the ball take to reach to the height of $30 m ?$
$\text{OR}$
$(iii) (b)$ Find the two different values of $t$ when the height of the ball was $20 m.$
→
A helicopter lifts up 1000 feet over an island and spots a swimmer that need to be rescued. Using a distant land mark, the helicopter pilot determines the angle of depression.
Image
(i) As the angle of depression increases what will be the effect?
(a) The helicopter gets further from the island.
(b) The helicopter gets closer to the island.
(c) The swimmer gets closer to the island.
(d) The swimmer gets further from the island.
(ii) How does the swimmer's distance from island changes as the angle of depression is halved from $60^{\circ}$ to $30^{\circ}$ ?
(a) The swimmer's distance decreases to less than a quarter of his starting distance.
(b) The swimmer's distance from the island doubles
(c) The swimmer's distance from the island increases three times.
(d) The swimmer's distance from the island is halved.
(iii) For which angle of depression both the helicopter and swimmer's will be at same distance?
(a) $30^{\circ}$ $\qquad$ (b) $45^{\circ}$ $\qquad$ (c) $60^{\circ}$ $\qquad$ (d) $90^{\circ}$
(iv) Let the swimmer start out 1019 ft . from the island. If he swims half of the distance, what is angle of depression?)
(a) nearly $30^{\circ}$ $\qquad$ (b) nearly $45^{\circ}$ $\qquad$ (c) nearly $60^{\circ}$ $\qquad$ (d) nearly $90^{\circ}$
→
Read the text carefully and answer the questions:
The students of a school decided to beautify the school on an annual day by fixing colourful flags on the straight passage of the school.They have $27$ flags to be fixed at intervals of every $2$ metre. The flags are stored at the position of the middlemost flag.Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time.
Image
$(a)$ How much distance did she cover in pacing $6$ flags on either side of center point?
$(b)$ Represent above information in Arithmetic progression
OR
How much distance did she cover in completing this job and returning to collect her books?
$(c)$ What is the maximum distance she travelled carrying a flag?
→
A man standing on the deck of a ship, which is 8m above water level. He observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°. Calculate the distance of the hill from the ship and the height of the hill.
→
Manpreet Kaur is the national record holder for women in the shot-put discipline. Her throw of 18.86 m at the Asian Grand Prix in 2017 is the biggest distance for an Indian female athlete. Keeping her as a role model, Sanjitha is determined to carn gold in Olympics one day. Initially her throw reached 7.56 m only. Being an athlete in school, she regularly practiced both in the mornings and in the evenings and was able to improve the distance by 9 cm every week. During the special camp for 15 days, she started with 40 throws and every day kept increasing the number of throws by 12 to achieve this remarkable progress.
Image
(i) How many throws Sanjitha practiced on $11^{\text {th }}$ day of the camp?
(ii) What would be Sanjitha's throw distance at the end of 6 months?
(iii) When will she be able to achieve a throw of 11.16 m ?
(iv) How many throws did she do during the entire camp of 15 days?
→

A group of mosquitoes were buzzing around in the playground at the evening. The playground is
considered in the region of the cartesian coordinate system where we mark a point on a graph by
how far along and how far up it is. The left-right (horizontal) direction is commonly called X-axis.The up-down (vertical) direction is commonly called Y-axis. Now, if two mosquitoes travel by the same path of coordinates, they will eventually collide and could not fly ahead. So, to ensure that each mosquito has its own unique path of travel. Refer the point O as origin.

(i)What will be the coordinates for the mosquito that flies in the middle of the playground ?
(ii)What is the distance between the two mosquitoes marked on the graph ?
OR
What is the difference between the distance of the two points marked on the graph
(iii) What is the value of ordinate for the mosquito flying just 1 unit below (4,3) ?
→
Basketball and Soccer are played with a spherical ball. Even through an athlete dribbles the ball in both sports, a basketball player uses his hands, a soccer player uses his feet. Usually, a soccer is played outdoors on a large field, the basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing a quadratic polynomial.
Image
(i) The shape of the path traced shown in Fig. is
(a) Spiral $\qquad$ (b) Ellipse $\qquad$ (c) Linear $\qquad$ (d) Parabola
(ii) If $p(x)=a x^2+b x+c$ is the parabola representing the graphs shown in Fig. then
(a) $a=0$ $\qquad$ (b) $a<0$ $\qquad$ (c) $a>0$ $\qquad$ (d) $a \geq 0$
(iii) The polynomial representing the graph shown in Fig. 2.8 has
(a) no zero $\qquad$ (b) one zero $\qquad$ (c) two zeroes $\qquad$ (d) three zeroes
Image
(iv) The three zeroes of the polynomial representing the above graph in Fig. 2.8 are
(a) $2,3,-1$ $\qquad$ (b) $-2,3,1$ $\qquad$ (c) $-3,-1,2$ $\qquad$ (d) $-2,-3,-1$
→
Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two Sections A and B. Tower is supported by wires from a point $O$.
Distance between the base of the tower and point O is 36 cm . From point O , the angle of elevation of the top of the Section B is $30^{\circ}$ and the angle of elevation of the top of Section $A$ is $45^{\circ}$.
Image
Based on the above information, answer the following questions:
(i) Find the length of the wire from the point O to the top of Section B.
(ii) Find the distance $A B$.
OR
Find the area of $\triangle OPB$.
(iii) Find the height of the Section A from the base of the tower.
→
The chain and gears of bicycles or motorcycles or belt around pulleys are some real-life illustrations of tangents to circles.
Image
(i) $P I$ and $P A$ are tangents to the circle from point $P$. If arc $I Z A$ subtends an angle $240^{\circ}$ at the centre of the circle, then $\angle I P A=$
(a) $120^{\circ}$ $\qquad$ (b) $90^{\circ}$ $\qquad$ (c) $60^{\circ}$ $\qquad$ (d) $30^{\circ}$
(ii) If $I P=15 cm$, then $A I=$
(a) 7.5 cm $\qquad$ (b) 15 cm $\qquad$ (c) 30 cm $\qquad$ (d) 18 cm
(iii) If $I P=21 cm$ and measure of $A P$ is $x^2+5$, then $x=$
(a) 4 $\qquad$ (b) 16 $\qquad$ (c) $\sqrt{26}$ $\qquad$ (d) $\sqrt{30}$
(iv) $\angle O I P+\angle A P O=$
(a) $90^{\circ}$ $\qquad$ (b) $60^{\circ}$ $\qquad$ (c) $120^{\circ}$ $\qquad$ (d) $150^{\circ}$
→
Ajay wants to host a party on his $50^{\text {th }}$ birthday in a large banquet hall having a certain number of chairs. He wants that guests should sit in different groups like in pairs, triplets, quadruplets, fives and sixes etc. When the banquet hall manager arranges chairs in such pattern like in $2^{\prime S}, 3^{\prime S}, 4^S, 5^{\prime S}$ and $6^{\prime S}$ then $1,2,3,4$ and 5 chairs are left respectively. But, when he arranges in groups of $11^{\prime} S$ no chair is left.
(i) How many chairs are in the banquet hall?
(a) 407 $\qquad$ (b) 209 $\qquad$ (c) 539 $\qquad$ (d) 149
(ii) If three chairs are removed, then the remaining chairs can be arranged in groups of
(a) $2^{\prime s}$ $\qquad$ (b) $3^{\prime s}$ $\qquad$ (c) $4^{\prime s}$ $\qquad$ (d) $2^{\prime s}$
(iii) If one chair is added, then the total number of chairs can be arranged in groups of
(a) $2^{\prime s}$ $\qquad$ (b) $3^{\prime s}$ $\qquad$ (c) $4^{\prime s}$ $\qquad$ (d) $11^{\prime s}$
(iv) If one chair is added to the total number of chairs, how many chairs will be left when arranged in groups of $11^s$
(a) 1 $\qquad$ (b) 2 $\qquad$ (c) 3 $\qquad$ (d) 4
→