From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm find the radius of the circle.
Answers
[tex]\large\bold{{Question :}}[/tex]
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm find the radius of the circle.
[tex]\large\bold\red{\underline{Solution :-}}[/tex]
Here, O is the center of the circle.
⟼ Given :
OQ = 25 cmPQ = 24 cm⟼ To Find : We have to find the radius OP.
Since QP is tangent, OP perpendicular to QP.
(Since, Tangent is Perpendicular to Radius ⠀⠀⠀⠀⠀⠀⠀at the point of contact)
So, ∠OPQ=90°
⟼ By Applying Pythagoras Theorem :
OP² + RQ² = OQ²
OP² + (24)² = (25)²
OP² = 625 - 576
OP² = 49
OP = √49
OP = 7 cm
Hence, The Radius is 7 cm
⠀⠀
⠀
-MissAbhi
Here after drawing the diagram for the question we came to knew that the length of line OQ is 25 cm and length of line PQ is 24 cm.
(Angle OP is of 90°)So line OQ is hypotenuse , line OP is perpendicular , line PQ is base.
Let us simply apply the concept of Pythagoras theorem to find out the length of line OP.
Base (PQ) = 24 cm Hypotenuse (OQ) = 25 cm Perpendicular (OP) = ?[tex]: \: \implies \: \sf{(Hypotenuse) {}^{2} \: = \: (Base) {}^{2} \: + \: (Perpendicular) {}^{2} } \\ \\ : \: \implies \: \sf{(OQ) {}^{2} \: = \: (OP) {}^{2} \: + \: (PQ) {}^{2} } \\ \\ : \: \implies \: \sf{(25) {}^{2} \: = \: (OP) {}^{2} \: + \: (24) {}^{2} } \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: (25) {}^{2} - \: (24) {}^{2}} \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: (25 \times 25) - \: (24 \times 24)} \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: (625) - \: (576)} \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: 625 - \: 576} \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: 49} \\ \\ : \: \implies \: \sf{OP \: = \: \sqrt{49} } \\ \\ : \: \implies \: \red{\bf{OP \: = \: 7}}[/tex]
★ Therefore,
Radius of the circle is of 7 cm.
Related Questions
which number has a 9 with a value ten times greater than the 9 in 4 903
Answers
Answer:
49030
Step-by-step explanation:
we multiply it by ten so
4903×10=49030
Hi can someone please help me
Answers
Answer:
Last and second lastv
Step-by-step explanation:
According to the rational factorization.
4. The number of feet in a yard can be represented by a graph. Circle the graph(s) that could
be used to represent the number of feet, y, in x yards.
GRAPH A
GRAPH B
GRAPH
GRAPHD
27
26
21
18
LS
60
54
48
42
36
30
20
18
12
135
12
105
9
75
6
60
54
40
42
36
30
24
18
12
9
45
3
3
15
6
Answers
help me please…………..
Answers
answer: b
explained below
Since both terms are perfect squares, factor using the difference of squares formula
Maggie takes three electives: art, Spanish, and creative writing. She calculated the mean absolute deviation of the points she earned throughout the year in each class. art: mean absolute deviation of 2.1
Spanish: mean absolute deviation of 0.8
creative writing: mean absolute deviation of 2.7
In which elective were her scores the most spread out?
Answers
Answer:
0.8 seconds sorry if im wrong
Step-by-step explanation:
{4x+y=9 and 5x +2y=9
use substitution method to find all solutions of the system of equations
(X,y)=
Answers
Answer:
x=3,y=-3
Step-by-step explanation:
Isolate x for 4x +y=9: x=9-y/4
Substitute x = 9-y/4
[5 x 9-y/4+2y =9]
Isolate y for (45+3y/4)=9:
y=-3
For x= 9-y/4
Substitute y = -3
x= 9-(-3)/4
9-(-3)/4=3
X=3
The solutions to the system of equations are:
x=3 y= -3
The point A(5.
7) is reflected over the
What are the coordinates of point B?
point (6,
6) and its
image is point B.
Answers
The point (6, 6) is the mid-point of A and B. Then the coordinate of the point B is (7, 5).
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Point A (5, 7) is reflected over the point (6, 6) and its image is point B. Then the point (6, 6) is the mid-point of the A and B. Then the coordinate of the point B will be
[tex]\rm (x_2 , y_2) = (2x -x _1, 2y - y_1)\\\\(x_2 , y_2) = (2 \times 6 - 5, 2 \times 6- 7)\\\\(x_2 , y_2) = (12-5,12-7)\\\\(x_2 , y_2) = (7, 5)[/tex]
More about the coordinate geometry link is given below.
https://brainly.com/question/1601567
#SPJ1
Find an equation of the line passing through the pair of points (3,5) and (6,11). Write the equation in the form Ax+By=C
Answers
Answer: (4,8)
Step-by-step explanation:
solve:
-0.4k-6=1.2
If you answer this you're a God
Answers
Answer:
The answer is k = -18
Step-by-step explanation:
This is so easy... so first you do -2k/5 - 6 = 1.2
-2k + 5(-6)/5 = 1.2
and then all that divided by 5
richard has two circular sprinklers to water his rectangular backyard as shown.
Answers
Answer:
109.88 ft² (nearest hundredth)
Step-by-step explanation:
Formulae
Area of a rectangle = width × lengthArea of a circle = πr²To find the area of the lawn that is not watered, subtract the area of the 2 circles from the area of the rectangle.
From inspection of the diagram
width of rectangle = 2rlength of rectangle = 4rarea = 512 ft²Substituting the values into the area of a rectangle formula, and solving for r:
⇒ 512 = 2r × 4r
⇒ 512 = 8r²
⇒ r² = 64
⇒ r = ±8
As distance is positive, r = 8 ft
Area of one circle = π8² = 64π ft²
Therefore,
Area not watered = area of rectangle - 2 × area of circle
= 512 - 2(64π)
= 109.88 ft² (nearest hundredth)
Find the equation of the tangent to the curve y = 4x³- 5x² + x - 3 at the point where it crosses the y axis.
Answers
Answer:
y = x-3
Step-by-step explanation:
When the graph of this equation crosses the y - axis , the value of x is = 0.
sub in zero to find this y value = -3
so the point is (0, -3)
Now find the drivative of this equation....the derivative tells you the slope of the original graph at any given point
derivative = 12x^2-10x+1 this , when x = 0 shows slope = 1
the equation then becomes y = (1) x -3 or just y = x-3
See image below
Answer:
-3
Step-by-step explanation:
put x= 0
pls help i need an A my mom is going to get mad at me pls help i will give 62 points
Answers
Answer:
I would say the second one
Step-by-step explanation: Good luck! :)
Hey can somebody help me on this?
Answers
Answer: 7
Step-by-step explanation: g = 8 ( given ) g/2+3 plugging the value of g 8/2+3
8+3x2
2
8+6
2
14
7
= 2
Pablo's father is 4 years older than his mother and Pablo is a third his mother's age.
If their combined age is 74 years
Answers
Explanation:
5. Change the following mixed numbers to improper
fractions.
a. 3 5/6
b. 2 7/8
C. 5 1/5
D. 7 1/9
Answers
b.23/8
c.26/5
d.64/9
A sum of money was distributed among some boys. Had there been two boys more, each would have received Rs. 10 less. Had there been two boys less, each would have received Rs. 15 more. Find the number of boys and the sum received by each.
Answers
Given -
A sum of money was distributed among some boys.Had there been two boys more, each would have received Rs. 10 less.Had there been two boys less, each would have received Rs. 15 more.To find -
the number of boys and the sum received by each.Explanation -
Here as we are required to find the value of two different individuals hence first we will from 2 linear equations into two variables (taking each to be value as x and y or whatever you like, I will take them as a and b) will solve the equation by any method of your choice (explanation for them is in the link, below, it is given by the same me)
https://brainly.com/question/27161912?utm_source=android&utm_medium=share&utm_campaign=question
Solution -
Let the sum of money that was given to each boy be a and the number of boys be b. Hence, the total no. of money distributed to b no. of boys is ab.
According to the question,
Scenario 1 -
➡ (a + 2)(b - 10) = ab
Solving it further,
➡ a(b - 10) + 2(b - 10)= ab
➡ ab - 10a + 2b - 20= ab
Cancelling ab,
➡ 10a - 2b + 20 = 0
➡ 10a = 2b - 20
➡ a = 2(b - 10)/10
➡ a = (b - 10)/5
Scenario 2 -
➡ (a - 2)(b + 15) = ab
Solving it further,
➡ a(b + 15) - 2(b + 15)= ab
➡ ab + 15a - 2b - 30= ab
Cancelling ab,
➡ 15a - 2b - 30 = 0
Substituting the value of a in the equation,
➡ 15{(b - 10)/5} - 2b - 30 = 0
➡ 3(b - 10) - 2b - 30 = 0
➡ 3b - 30 - 2b - 30 = 0
➡ 3b - 2b -60 = 0
➡ b = 60
Substituting the value of b in a = (b - 10)/5,
➡ a = (60 - 10)/5
➡ a = 50/5
➡ a = 10
[Here we have used the substitution method]
Henceforth, the total number of boys is 60 and the sum received by each is Rs. 10 .
5* 3 1/3 I have to have my math done in an hour and I don’t know this
Answers
16.65... .... ..... ...
Answer: 16.65
Step-by-step explanation:
1/3 is equivalent to the decimal value .33
so, use the equation:
5x(3+.33) or 5x3.33, which equals 16.65
what's the estimate of 6.48 + 9.34
Answers
Answer:
6+9=15
Step-by-step explanation:
hope this helps :D
13.
Hamza made 6 calls in
one day. Each call cost the
same amount of
money. The next day he made a
call that cost $4. Which expression
represents the total cost of the calls Hamza made during the two
days?
Answers
Answer:
6x +4 where x is amount for standard call
Step-by-step explanation:
Answer:
4c+6
Step-by-step explanation:
Right on my test
Find two positive numbers whose difference is 27 and whose product is 874.
Answers
Please help. I need the answer
Answers
Answer:
B
Step-by-step explanation:
[tex]m-5\neq 5-m[/tex]
The others follow the rules of the commutative property of multiplication/addition.
Answer:
B
m - 5
Step-by-step explanation:
1) division
2) m - 5 . Since subtraction is not commutative
Ryan invested $257 in an account paying an interest rate of 3.9% compounded weekly.
What is the equation?
Answers
Answer:
The equation is 257/x = x/3.9
Step-by-step explanation:
using appropriate property find -2/5 ×1/5 + 2/5 × 1/5
Answers
Answer:
simply cut 5 and solve if no property needed but if needed use distributive
same homework. different question.
Answers
Answer:
Answer = B. Obtuse.
Step-by-step explanation:
Find the minimum value of X²+6X-5
Answers
Answer:
x = -3, y = -14
Step-by-step explanation:
Graph it
Graph it
Choose the graph that represents the equation y=x-2
Answers
Step-by-step explanation:
The choices are not given but the graph looks like the above picture.
Answer:
just use Desmos graphing calculator, it works great.
Step-by-step explanation:
Which of the following options have the same value as 10 % , percent of 33?
Answers
Answer:
3.3
Step-by-step explanation:
33 x .10 = 3.3
Bilquis owns a small business selling used books. She knows that in the last week 49 customers paid cash, 42 customers used a debit card, and 32 customers used a credit card.
Based on these results, express the probability that the next customer will pay with a credit card as a decimal to the nearest hundredth.
Answers
The probability that the next customer will pay with a credit card will be 0.26 or 26%.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Bilquis owns a small business selling used books. She knows that in the last week 49 customers paid cash, 42 customers used a debit card, and 32 customers used a credit card.
Then the probability that the next customer will pay with a credit card will be
[tex]\rm P = \dfrac{32}{123}\\\\ P = 0.26[/tex]
More about the probability link is given below.
https://brainly.com/question/795909
#SPJ1
Answer:
The answer is .26
Step-by-step explanation:
32/123
0.260162...
A factory makes aquariums. Each aquarium is in the shape of a triangular prism, as shown below. If the factory makes 288 aquariums, how much water will be needed to fill all of them (in cubic feet)?
Answers
Answer:
384
Step-by-step explanation:
Solve and show your work for each question.
Note: Remember per the rule of 9s if you have a repeating and non-repeating component you need to handle them separately.
What is 0.47 expressed as a fraction in simplest form?
What is 0.4¯7 expressed as a fraction in simplest form?
What is 0.¯47 expressed as a fraction in simplest form?
Answer:
show work on how you did it
Answers
The computation of the figure illustrates that 0.47 expressed as a fraction in simplest form is 43/90.
How to compute the fraction?From the information given, let a = 0.47. Now 10a = 4.777 .... equation i
100a = 47.77 ..... equation ii
Subtract equation i from ii
100a - 10a = 47 - 4
90a = 43
Divide both side by 90
90a/90 = 43/90
a = 43/90
Learn more about fractions on:
https://brainly.com/question/78672