Two tangents drawn to a circle from a point outside it, are equal in length.prove it.

Answers

Answer 1
Given: A circle with centre O; PA and PB are two tangents to the circle drawn from an external point P.
To prove: PA = PB
Construction: Join OA, OB, and OP.
It is known that a tangent at any point of a circle is perpendicular to the radius through the point of contact.
OA⊥PA
OB⊥PB
In △OPA and △OPB
∠OPA=∠OPB (Using (1))
OA=OB (Radii of the same circle)
OP=OP (Common side)
Therefor △OPA≅△OPB (RHS congruency criterion)
PA=PB
(Corresponding parts of congruent triangles are equal)
Thus, it is proved that the lengths of the two tangents drawn from an external point to a circle are equal.
The length of tangents drawn from any external point are equal.
So statement is correct

Related Questions

What is the lateral area of the pyramid shown below?
26 ft.
20 ft.
20 ft.

Answers

Answer:

Your correct answer is 1514.27

Step-by-step explanation:

Here is my step by step for you!

plzz help steps if possible if not its ok j=i just need to pass this class

Answers

Answer:

[tex]\text{(B) }\cos 40^{\circ}=\frac{x}{60}[/tex]

Step-by-step explanation:

In any triangle, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse (longest side) of the triangle. (a/h)

The angle marked 40 degrees has an adjacent side of [tex]x[/tex] and the hypotenuse of the triangle is 60.

Therefore, we have the equation:

[tex]\boxed{\cos 40^{\circ}=\frac{x}{60}}[/tex]

Find the domain and explain pls and thankyouuu

Answers

Answer:

[tex]x\neq 0\\x\neq 2[/tex]

Step-by-step explanation:

simplify the equation: [tex]\frac{6}{x(x-2)}[/tex]

Since the denominator can never equal 0, x can never equal 0 or 2.

Meaning that the domain is any x-value other than 0 or 2.

Show and explain all of the steps used in order to simplify the following rational expression 3x^(2)-3x / 3x^(3)-6x^(2)+3x to 1 / x-1.

Answers

Answer:

3x^2 + x^4 - x^3 + 3 - 6x

Step-by-step explanation:

Find Least Common Multiplier of 3x^(2)-3x / 3x^(3)-6x^(2)+3x to 1 / x-1

3x^2 - 3 . x/3 x^3 - 6x^2 + 3x

Apply exponent rule: a^b + c = a^b a^c

x^2 = xx, x^3 x/3 = xx^2, x^2 = xx

= 3xx - 3xxx - 6xx + 3x

Rewrite -6 as 2 . 3

= 3xx - 3xxx + 2 . 3xx + 3x

Factor out common term 3x

= 3x(x - x^2(x/3) -2x + 1)

= 3x(- x^3/3 - x + 1)

Multiply each factor with the highest power:

(- x^3/3 - x + 1) . 3 . (1/x - 1\) . x

Simplify

3x^2 + x^4 - x^3 + 3 - 6x

Six teachers and 12 students volunteer for a committee to discuss extra-curricular activities. How many committees of 5 people can be made if:

a) there must be exactly 3 students on the committee

b) there must be at least one teacher and at least one student on the committee

Answers

Answer:

a) 11,880

b) 7,770

Step-by-step explanation:

The number of teachers that volunteer = 6 teachers

The number of students that volunteer = 12 students

The number of people in the committee = 5 people

a) The exact number of student on the committee = 3 student

Therefore, the number of teachers in the committee of 5 = 5 - 3 = 2

The number of teachers in the committee = 2 teachers

We get;

The number of committees that can be made = ₁₂C₃ × ₆C₂ = 792×15 = 11,880

b) When there is at least one teacher and at least one student on the committee, we have;

₁₂C₄ × ₆C₁ + ₁₂C₃ × ₆C₂ + ₁₂C₂ × ₆C₃ + ₁₂C₁ × ₆C₄ = 7,770

The number of committees having at least one teacher and at least one student = 7,770

Candice bought 6 dozen eggs and broke 9 eggs how many eggs did she have left

Answers

Answer:

63

Step-by-step explanation:

12x6=72

72-9=63

the answer is 63

Answer: 63 eggs


Step 1: Find initial amount of eggs

Before we can solve for how many eggs are left, we must first find out how many eggs Candice initially had. We are told she bought six dozen eggs. Since a dozen is twelve, we can find out how many eggs she had by multiplying twelve and six. Let’s do this now.

6×12= 72

Step 2: Find solution

Now let’s solve for how many eggs Candice has left. We know that she bought 72 eggs, and that she broke 9. To find the answer, we need to subtract 9 from 72.

72-9= 63


Hope this helps! Comment below for more questions.

What's the slope of (2, 1) (4,5)

Answers

Answer:

[tex]\displaystyle m = 2[/tex]

General Formulas and Concepts:

Algebra I

Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

Point (2, 1)

Point (4, 5)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute in points [Slope Formula]:                                                              [tex]\displaystyle m = \frac{5 - 1}{4 - 2}[/tex]Subtract:                                                                                                            [tex]\displaystyle m = \frac{4}{2}[/tex]Simplify:                                                                                                             [tex]\displaystyle m = 2[/tex]

Create a line that is parallel to A⁢B↔ and passes through point C.​

Answers

Draw 2 lines parallel to each other (AB and line B). Draw a point on line B and label it "C"

A group of 2 adults and 4 children spent $38 on tickets to a museum. A group of 3 adults and 3 children spent $40.50 on tickets to the museum. Based on this information, how much is an adult ticket, and how much is a child ticket?

Answers

Answer:

adult $8.00

child $5.50

Step-by-step explanation:

Let the price of 1 adult ticket = x.

Let the price of 1 child ticket = y.

2x + 4y = 38

3x + 3y = 40.5

Multiply the first equation by 3. Multiply the second equation by -2. Then add them.

         6x + 12y = 114

(+)      -6x - 6y = -81

-----------------------------

                  6y = 33

y = 33/6

y = 5.5

2x + 4y = 38

2x + 4(5.5) = 38

2x + 22 = 38

2x = 16

x = 8

Answer:

adult $8.00

child $5.50

Answer:

An adult ticket is $8.00 and a child's ticket is $5.50.

Step-by-step explanation:

We form a system of 2 equations and solve them.

Let a be the price of adult ticket and c the price of a child's.

2a + 4c = 38         (A)

3a + 3c = 40.5      (B)

Multiply equation A by 3 and equation B by -2:

6a + 12c = 114

-6a - 6c = -81        Adding these 2 equations:

0 + 6c = 33

c = 33/6 = 5.5.

Now we substitute for c in equation A:

2a + 4(5.5) = 38

2a = 38 - 22

2a = 16

a = 6.

Let's now check these results by substitution in equation B:

3a + 3c = 40.5

3(8) + 3(5.5) = 24.0 + 16.5 = 40.5

- so it checks out.

The fraction 9/7 is equivalent to?

Answers

9/7 is equivalent to 18/14 or 27/21 or 36/28 etc

Answered by Gauthmath must click thanks and mark brainliest

Line CD passes through points C(3, 5) and D(6, 0). What is the equation of the line CD in standard form?

Answers

Answer:

the answer is 5x - 3y = 30!!

Derek had a bill of $29 last month on he Call-a-Lot Plan. How many minutes did he use?

Answers

it depends on how much it costed per minute if it was a dollar a minute then it would be 29 minutes

Matt is making cookies. He adds 3 over 4 cup of sugar to a bowl. He then removes two 1 over 8 cups of sugar. Which of the following best explains the amount of sugar left in the bowl?

Answers

Answer:

3/4 is equal to 6/8 2 1/8s is equal to 2/8

Answer:

Step-by-step explanation:

Hi Arianna!

3 over 4 cups of sugar = 3/4

Two one over eight cups of sugar = 2 1/8

Basically we’re trying to find out the amount of sugar left in the bowl.

Matt adds 3/4 cup of sugar

Then removes 2 1/8 cups of sugar

1
Work out the area of the shape:
3cm
6cm
2cm
2cm

Answers

Answer:

24 cm

Step-by-step explanation:

6*2+3*4=?

12+12

24 cm

Find the value x ……….

Answers

Answer: 6 because it more than thd base and less than the other triangles leg

Step-by-step explanation:

Answer:

[tex]4\sqrt{5}[/tex]

Step-by-step explanation:

[tex]x^2 = y^2 + 25[/tex]

[tex]\frac{y}{11} = \frac{5}{y}[/tex]  

[tex]y^2 = 55[/tex]

[tex]x^2 = 80\\x = \sqrt{80} \\x= 4\sqrt{5}[/tex]

Question 8(Multiple Choice Worth 5 points) (01.01 MC) Which number line best show how to solve -4 - (-8)?​

Answers

The answer to your question is A

Answer:

4

Step-by-step explanation:

-4 - (-8) Note: a negative negative equals a positive. There for it is just the same as saying -4 + 8

What is the value of x?

Answers

Answer:

x is equal to give

Hope am correct

Answer:

x = 5.

Step-by-step explanation:

x / (x + 5) = (x - 2)/(x+ 1)

x(x + 1) = (x - 2)(x + 5)

x^2 + x = x^2 + 3x - 10

x = 3x - 10

-2x = -10

x = 5.

1) Se o 5o e o 9-o termos de uma PA são, respectivamente, 40 e 68, então a razão r da progressão é: a) r = 6 b) r = 7 c) r = 9 d) r = 11 e) r = 12 2) Inserindo-se 6 números entre 72 e 107, de modo que a sequência (72, a2, a3, a4, a5, a6, a7 ,107) seja uma progressão aritmética, tem-se a3 igual a: a) 78 b) 79 c) 80 d) 81 e) 82

Answers

Answer:

1) b) r = 7

2) e) 82

Step-by-step explanation:

Progressão aritmética:

Em uma progressão aritmética, a diferença entre termos consecutivos é sempre a mesma, chamada de razão.

O n-ésimo termo de uma PA é dado por, tomando o primeiro termo como referência:

[tex]a_n = a_1 + (n-1)r[/tex]

Tomando o m-ésimo termo como referência, tem-se que:

[tex]a_n = a_m + (n-m)r[/tex]

1) Se o 5o e o 9-o termos de uma PA são, respectivamente, 40 e 68, então a razão r da progressão é:

[tex]a_5 = 40, a_9 = 68[/tex]. Então:

[tex]a_n = a_m + (n-m)r[/tex]

[tex]68 = 40 + 4r[/tex]

[tex]4r = 28[/tex]

[tex]r = \frac{28}{4} = 7[/tex]

Então a resposta correta é dada pela alternativa b.

2) Inserindo-se 6 números entre 72 e 107, de modo que a sequência (72, a2, a3, a4, a5, a6, a7 ,107) seja uma progressão aritmética, tem-se a3 igual a:

O primeiro termo é [tex]a_1 = 72[/tex] e o oitavo termo é [tex]a_8 = 107[/tex]. Com isso, é possível encontrar a razão.

[tex]a_n = a_1 + (n-1)r[/tex]

[tex]107 = 72 + 7r[/tex]

[tex]7r = 35[/tex]

[tex]r = \frac{35}{7} = 5[/tex]

Então, o terceiro termo é:

[tex]a_3 = a_1 + 2r = 72 + 2(5) = 82[/tex]

Logo, a resposta correta é dada pela alternativa e.

Please help
I am giving all my points for this (15 points)
Select all input values for which g(x)=8.
Choose all answers that apply:
(Choice A)
x=−4
(Choice B)
x=6
(Choice C)
x=9
(Choice D)
None of the above

Answers

Answer:

D. none of the above

Step-by-step explanation:

If g(x)=8 is the only equation, then none of the answers are correct. The correct answer would have been 8 because 8=8.

A stationer buys a gel pen Rs 20 and sells it at 20% profit.For what price should he buy it so that he can make 25% profit by selling for the same selling price.

Answers

Answer:

Current selling price = Rs 20 × 120 %

= Rs 24

Cost price should be [100 ÷ 125 ] × 24

= Rs 19.20

If a zero is
, then the graph of its function only touches the x–axis at that zero.

Answers

Answer:

Step-by-step explanation:

Yes. The zeroes of a graph are the values of x where the graph touches (or crosses) the x-axis.

A student buys 5-cent, 10-cent, and 15-cent stamps, with a total value of $6.70. If the
number of 5-cent stamps is 2 more than the number of 10-cent stamps, while the
number of 15-cent stamps is 5 more than one half the number of 10-cent stamps, how
many 15-cent stamps did the student obtain?

Answers

The value of the 10 cent stamps is, as you said, , the value of the 5 cent stamps is and the value of the 15 cent stamps is 15(0.5n + 5). These three values add up to the total value of the stamps, namely $6.70.

10n + 5(n+2) + 15 (1/2n + 5) = 6.70

10n +5n + 10 + 15/2n + 75 =670

10n + 5n + 15/2n =585

20n + 10n + 15n = 1170

45n = 1170

N=26

What is the rate of change of the function shown on the graph? Round to the nearest tenth.

Answers

The answer is (B) which is 2.5

3(5-4)+2(5)-5 squared

Answers

the answer should be -12 if I did the math right.

Step-by-step explanation:

3*1+10-5^2(we subtract 5 from 4 first because it was inside bracket)

3+10-25(Square of 5 is 25)

-12(subtracting the above equation 12 comes)

Can someone help me with this math homework please!

Answers

Answer:

negative

Step-by-step explanation:

Let,

x1 = 0

x2 = 1

y1 = 50

y2 = 44

Formula : -

Slope = ( y2 - y1 ) / ( x2 - x1 )

Slope

= ( 44 - 50 ) / ( 1 - 0 )

= - 6 / 1

= - 6

- 6 is a negative number.

So, the slope is negative.

Help pls appreciate it pls

Answers

Answer: D.

Step-by-step explanation:

If we know that 1 side equal along with 1 angle is equal to the other triangles angle and side. Than only one answer really stands out (at least to me) if that makes any sense

Hope this helps

:)

ASAP please help meeeeeeeeeeeeeee

Answers

Answer:

7/10

(-4×-7)/(5×8)

=28/40

=7/10

Find the measure of one exterior angle for the following regular polygon

Answers

72, all exterior angles of a regular polygon add up to 360, there are five exterior angles so you would do 360÷5 which is 72

Can you answer this math homework? Please!

Answers

Answer:

1

Step-by-step explanation:

Answer:

They are both correct

Step-by-step explanation:

They started isolating different variables but essentially they have found the same answers just with different isolated variables, thus their answers look different, but in reality, are the exact same.

We can test by plugging 5 in for x, and 15 in for y.

Jared:

[tex]y=x+10\\[/tex][tex]15=5+10[/tex][tex]15=15[/tex]

Nicole:

[tex]x=y-10[/tex][tex]5=15-10[/tex][tex]5=5[/tex]

Equations are equal.

x-(x-(x-y³)) use x=9, and y=1

Answers

9-(9-(9-1))
9-(9-8)
9-1
8

Answer:

The answer: 8

Step-by-step explanation:

x-(x-(x-y³))

x=9 , y=1 —> 9 - (9-(9-1³)) —> 9 - (9-(8))—> 9 - ( 1) —> =8

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