Mathematics High School

Two tangents PQ and PR are drawn to a circle with center o from an external point P. prove that
Angle QPR = 2 angle OQR

Answers

Answer 1

Answer:

Refer the digram & explanation.

Step-by-step explanation:

GIVEN :-

Tangents PQ & PR drawn to a circle with center O from an external point P.

TO PROVE :-

∠QPR = 2∠OQR

CONSTRUCTION :-

QR joined.

FACTS TO KNOW BEFORE SOLVING :-

(Angle at which tangents are inclined to each other from the external point) + (Angle the tangents subtend at the center of the circle) = 180°.

PROCEDURE :-

∠QPR + ∠QOR = 180°

⇒ ∠QOR = 180° - ∠QPR

In ΔQOR , OQ = OR (∵ Radii of the circle are equal)

⇒ ΔQOR is an isosceles triangle (∵ OQ = OR i.e. two sides of the triangle are equal.)

⇒ ∠OQR = ∠ORQ (∵ In an isosceles triangle , the base angles are equal)

So,

∠QOR + ∠OQR + ∠ORQ = 180°

⇒ ∠QOR + 2∠OQR = 180°  (∵ ∠OQR = ∠ORQ)

⇒ 180° - ∠QPR = 180° - 2∠OQR  (∵ ∠QPR + ∠QOR = 180°)

⇒ -∠QPR = -2∠OQR  (∵ Cancelling 180° from both the sides.)

⇒ ∠QPR = 2∠OQR (Proved)

Two Tangents PQ And PR Are Drawn To A Circle With Center O From An External Point P. Prove That Angle

Related Questions

3. John is making a tent for the next camping trip. The tent is pictured below. How
much fabric does he need for the tent?
6 m
6 m
5 m
10 m
8 m

Answers

Answer:

the sides = 6 * 10 * 2 = 120 sq meters

front & rear triangle = .5 * 8 * 5 * 2 = 40 sq meters

total fabric needed = 160 square meters

that is NOT one of your answers but I think you may not have typed it correctly.  

Step-by-step explanation:

Q=2u2 - 5
(d) Find the value of Q when u=-3

Answers

Answer:

q=13

Step-by-step explanation:

u=-3

q=2u^2 - 5

q=2(-3)^2 - 5

q= 2(9) - 5

q= 18 - 5

q=13

Gia has 80 tiles each tile is white or blue she arranges the tiles in 8 equal rows each row has an equal number of white and blue tiles how many blue tiles are in each row

Answers

Answer:

5 blue and 5 white tiles per row

Step-by-step explanation:

80/8 =(10-this is the amount per row)then divide 10 by 2 to factor in your different different tiles)

Work Check:

80/8rows=10/2colors=5 this means 5 blue and 5 white per row

What is 1 quarter of 72

Answers

Answer:

18

Step-by-step explanation:

72/4

answer
18
step by step
72/4

If a varies directly with x squared, and a=12 when x=6 find the constant variation, k

Answers

Answer:

k = 1/3

Step-by-step explanation:

a = kx²

12 = k * 6²

k = 12/36

k = 1/3

Answer: k = 1/3

Math question pls help

Answers

Answer:

190

Step-by-step explanation:

Find 19 on the x axis.

Go straight up until you hit the line representing the line made from a scatterplot.

Go horizontally to your left.

You should come to 190 and that's your answer.

Please help i will mark brainliest

Answers

Answer:

Step-by-step explanation:

2.5 is the answer

The dotted lines show how to cut the pie. Identify m∠LPM.
Please no links.

Whoever gives me a full explanation and answer without a link, I will mark as brainiest.

Answers

Answer:

m∠LPM = 60°

Step-by-step explanation:

The function f is given in three equivalent forms.
Which form most quickly reveals the vertex?
Choose 1 answer:
f(x) = 3x^2+ 36x + 33
f(x) = 3(x+6^2-75
f(x)=3(x+1)(x+11)
What is the vertex?

Answers

Answer:

Step-by-step explanation:

Look what happens when you factor the 3 out of the first choice:

f(x) = 3x^2+ 36x + 33 = f(x) = 3(x^2+ 12x) + 11

We can "complete the square:"  x^2 + 12x becomes x^2 + 12x + 36 - 36, which, in turn, becomes (x + 6)^2 - 36

so that the original f(x) becomes   f(x) = 3(x + 6)^2 - 36 + 33, or

f(x) = 3(x + 6)^2 - 3

Comparing this to

f(x) =a(x - h)^2 + k reveals that h = -6 and k = -3.  Thus, the vertex is at (-6, -3).

solve for x given the area of the rhombus is 340 cm squared

Answers

Answer:

17

Step-by-step explanation:

340/20=17

The price of a watch was increased by 20% to £162.
What was the price before the increase?

Answers

Answer:

The answer is 135

Step-by-step explanation:

We can use formula: 162...120% since the price was increased by 20% which means it is 120%

So: 162...120%

x.... 100%

120x = 16200 => x = 135


Help pls and no links

Answers

Answer:

4x plus 1 I think I'm not 100 percent sure though.

Rachel's car has a 12 gallon gas tank and
she uses about 0.5 gallons per day driving to
school. Write an equation describing the
number of gallons of gas, g, Rachel has in
her car and the number of days, d, she has
driven to school.


please help meeee

Answers

Answer:

g=dx

Or, if you'r wanting the solved equation..

12 = 0.5 x 24

Step-by-step explanation:

If she has 12 gallons in her tank and you look at what it's asking us to do, "..number of gallons of gas, g" pairs up with the 12 gallons while the 0.5 gallons used per day pairs with "...the number of days, d, she has driven to school."

Hope this helped!

what's this 2(n+1)−3

Answers

Answer:

Step-by-step explanation:

Solution

2-1

Please help. Will mark brainliest!!!!

A bus traveled 744 miles between two cities. The bus travels at a speed of 48 mph. Write a multiplication equation and then solve it to find out how many hours it took for the bus to arrive at its destination

Answers

Answer:

not sure

Step-by-step explanation:

can someone help me answer this

Answers

The answer is hopefully this helps!

which elapent weight 2.85 tons round to the nearst hundreth

Answers

2.9 because if you look at place value, behind the decimal it goes, tenths hundredths thousandths, and so on
Then you go to hundredths and see that it is 5. If it is 5 or up, you round up, and if it is 4 or lower, round down
So in this case, 2.85 would be rounded to 2.9

Please I need help with this math problem I would appreciate it a lot!

Answers

Answer:

4x^2 -3 + 1/x

Where ;

p(x) =( 4x^2 -3) and k = 1

Step-by-step explanation:

Here, we want to divide the given polynomial

To get this, we can use the method of long division

P(x) will be the quotient of the division, while k will be the remainder of the division

We can see the long division used in as seen in the attachment

So, we have the result as;

4x^2 -3 + 1/x

Where ;

p(x) = 4x^2 -3 and k = 1

Marking brainliest!

What is your favorite color, and if you were to describe your favorite color as a person, how would you describe it?

Answers

Answer:

Pink

Step-by-step explanation:

Bubbly,sweet,nice,kind

Answer:

my favorite color is sky blue. sky blue as a person is calm and soft, she has a soothing voice and is always kind


5-7:
Question Help
A nursery owner buys 8 panes of glass to fix some damage to his greenhouse. The 8 panes cost
$20.40. Unfortunately, he breaks 3 more panes while repairing the damage. What is the cost of
another 3 panes of glass?

Answers

The 3 panes would cost $7.65.
The answer is 7.65
Hope this helps!

Can anybody please help me on these notes?

Answers

Answer:

the y intercept will be at (0,-1) and to graph it just go up 6 and over 1 to the right and then go down 6 and 1 to the left

Step-by-step explanation:

hope this helps

Please help- will give brainlist

Answers

Answer:

No its C sorry

Step-by-step explanation:

Answer:

The answer is (c) 25π

Step-by-step explanation:

Area =πr²

r=diameter÷2

10÷2=5

Area=π * 5²

Area =25π

Solve and graph the following inequality:
x + (-15) > 12

Answers

Answer:

x>27

Step-by-step explanation:

x−15>12

Step 1: Add 15 to both sides.

x−15+15>12+15

x>27

hope it help

Amanda is pumping water into an aquarium at a rate of 12 liters per minute the aquarium had 42 liters of water in it before she started her goal is given by 13x+42<_234 where x is the number of minutes she pumps water into the aquarium

Answers

Answer:

Let x represent minutes.

The inequality derived from the question is...

58 > 18 + 5x

Solve for x...

58 > 18 + 5x

58 - 18 > 5x

40 > 5x

40/5 > x

8 > x

So it will take more than 8 minutes to have 58 liters.

Step-by-step explanation:

Please help me no one is helping me and I need help :(

Answers

Answer:

JK is longer

Step-by-step explanation:

You can kinda tell just by looking at it. Chord JK is closer to the center of the circle so it's longer.

Algebraic Method #2: Solving by substitution 2x + 8y = 20 y = 2​

Answers

2x+8y=20
2x+8•2=20
2x=20-16
2x=4
x=2
Check:
2•2+8•2=20
4+16=20
20=20
x=2 and y=2
Good luck.

find the value of x!

Answers

Answer:

I think it is

24.6

Answer:

           21.2

Step-by-step explanation:

[tex]x\times(x+ 28) = 20\times (20+32)\\\\x^2+28x-1040=0\\\\\ x=\dfrac{-28\pm\sqrt{28^2-4\cdot1\cdot(-1040)}}{2\cdot1}= \dfrac{-28\pm\sqrt{4944}}{2}\\\\x\approx21.2\quad or\quad x\approx-49.2[/tex]

x has to be >0 so the answer is 21.2

I need help with this problem

Answers

Answer:

72

Step-by-step explanation:

Given that the discriminant of a quadratic equation is 0, determine the number of real solutions.

Answers

If the discrimination is equal to 0, there is one real solution

Can someone help me with this? It’s due soon
-I’ll give brainliest

Answers

Answer:

I'M TURKISH I DONT KNOW.

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